JEE Mathematics Quadratic Equations MCQs

Question: The roots of the quadratic equation 2x² – 7x + 4 = 0 are -

• a) Irrational and different
• b) Rational and equal
• c) Imaginary and different
• d) Rational and different

Answer: Irrational and different

Question: The roots of the quadratic equation

x² – 2 (a + b) x + 2 (a² + b²) = 0 are -

• a) Imaginary and different
• b) Irrational and different
• c) Rational and equal
• d) Rational and different

Answer: Imaginary and different

Question: The roots of the equation x² – 2 √2 x + 1 = 0 are –

• a) Real and different
• b) Real and equal
• c) Imaginary and different
• d) Rational and different

Answer: Real and different

Question: The roots of the equation x² –3x – 4 = 0 are–

• a) Opposite and greater root in magnitude is positive
• b) Opposite and greater root in magnitude is negative
• c) Reciprocal to each other
• d) None of these

Answer: Opposite and greater root in magnitude is positive

Question: The roots of the equation 2x² – 3x + 2 = 0 are -

• a) Reciprocal to each other
• b) Both roots are zero
• c) None of these
• d) Negative of each other

Answer: Reciprocal to each other

Question: If equation x²-bx/ax-c = k-1/k+1 has equal and opposite roots then the value of k is -

• a) a-b/a+b
• b) a-b/a-b
• c) a+b/a-b
• d) None of these

Answer: a-b/a+b

Question:

• a) Rational and different
• b) Imaginary and different
• c) Real and equal
• d) Real and different

Answer: Rational and different

Question: If the roots of the equation x² + 2x + P = 0 are real then the value of P is -

• a) P≤1
• b) P≤2
• c) P≤3
• d) P≤4

Answer: P≤1

Question: If the product of the roots of the quadratic equation mx² – 2x + (2m – 1) = 0 is 3 then the value of m is -

• a) –1
• b) 1
• c) 2
• d) 3

Answer: –1

Question:

• a) 35
• b) 45
• c) 40
• d) None of these

Answer: 35

Question: If the equation (k – 2)x² – (k – 4) x – 2 = 0 has difference of roots as 3 then the value of k is-

• a) 3,3/2
• b) 3/2, 1
• c) 1,3
• d) 2, 3/2

Answer: 3,3/2

Question:

• a) b²-2ac/a²c²
• b) b²-2ac/ac
• c) b²-2ac/ac²
• d) None of these

Answer: b²-2ac/a²c²

Question: The roots of the equation x² – 2x – 8 = 0 are -

• a) 4, – 2
• b) – 4,– 2
• c) – 4, 2
• d) 4, 2

Answer: 4, – 2

Question: The roots of the equation x² – 4x + 1 = 0 are –

• a) 2 ± √3
• b) -2 ± 3
• c) 2, 4
• d) None of these

Answer: 2 ± √3

Question: The roots of the quadratic equation 7x² – 9x + 2 = 0 are -

• a) Rational and different
• b) Irrational and different
• c) Rational and equal
• d) Imaginary and different

Answer: Rational and different

More Questions................................

Question: The equation whose roots are 3 and 4 will be-

• a) x² – 7x + 12 = 0
• b) x² + 7x – 12=0
• c) x² – x + 12 = 0
• d) x² + 7x + 12 = 0

Answer: x² – 7x + 12 = 0

Question: The quadratic equation whose one root is 2 – i √3 is -

• a) x² – 4x + 7 = 0
• b) x² – 4x – 7=0
• c) x² + 4x – 7 = 0
• d) None of these

Answer: x² – 4x + 7 = 0

Question:

• a) x² – 4x + 4 = 0
• b) x² + 2x + 3 = 0
• c) x² + 4x + 1= 0
• d) x²– 4x –1= 0

Answer: x² – 4x + 4 = 0

Question:

• a) Both
• b) x² – 11x + 30 = 0
• c) (x – 3)² – 5 (x – 3) + 6 = 0
• d) None

Answer: Both

Question:

• a) x² – x – 2 = 0
• b) x² + x – 2 = 0
• c) x² + 2x – 8 = 0
• d) None of these

Answer: x² – x – 2 = 0

Question: If r and s are positive, then roots of the equation x² – rx – s = 0 are -

(1) real                  (2) imaginary
(3) opposite signs (4) both negative

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question: If a < b < c < d, then roots of equation (x – a)(x – c) + 2 (x – b) (x – d) = 0 are

(1) real (2) unequal
(3) imaginary (4) equal

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question: If p and q are roots of the equation x2 – 2x + A = 0 and r and s be roots of the equation x2 – 18 x + B = 0 if p < q < r < s be in A.P., then choose the correct options –

• a) 2 and 4 are correct
• b) 1, 2 and 3 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 2 and 4 are correct

Question:

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.

Question: Let a, b, c be real such that ax² + bx + c = 0 and x² + x + 1= 0 have a common root

Statement–1 : a = b = c
Statement–2 : Two quadratic equations with real coefficients can not have only one imaginary root common.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement-1 : If one roots is √5 - √2 then the equation of lowest degree with rational coefficient is x⁴–14x²+ 9 = 0
Statement-2 : For a polynomial equation with rational coefficient irrational roots occurs in pairs.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question: If f (x) is a quadratic expression which is positive for all real values of x and g(x) = f (x) + f '(x) + f "(x) , then for any real value of x-

• a) g (x) > 0
• b) g (x) < 0
• c) g (x) = 0
• d) None of these

Answer: g (x) > 0

Question: For real values of x, 2x² + 5x – 3 > 0, if-

• a) x > 1
• b) x < – 2
• c) x > 0
• d) None of these

Answer: x > 1

Question: For what value of m the expression y² + 4xy + 4x + my – 2 can be resolved into two rational factors-

• a) –1
• b) –2
• c) 1
• d) 2

Answer: –1

Question: The quadratic equation whose one root is 1/2 + √5 will be-

• a) x² + 4x – 1 = 0
• b) x² + 4x + 1= 0
• c) x² – 4x – 1 = 0
• d) None of these

Answer: x² + 4x – 1 = 0

Question:

• a) c,a,b
• b) a,b,c
• c) b,c,a
• d) None of these

Answer: c,a,b

Question: If the expression x²–11x + a and x² – 14x + 2a must have a common factor and a ≠ 0, then, the common factor is –

• a) (x – 8)
• b) (x – 3)
• c) (x – 6)
• d) None of these

Answer: (x – 8)

Question: If x is real then the value of the expression x²+14x+9/ x²+2x+3 between –

• a) –5 and 4
• b) – 4 and 5
• c) –3 and 3
• d) – 4 and 4

Answer: –5 and 4

Question:

• a) All these true
• b) –3 < x < 3/2
• c) x < –4
• d) x > 5/2

Answer: All these true

Question: The real values of a for which the quadratic equation 2x² – (a³ + 8a – 1) x + a²– 4a = 0 possesses roots of opposite signs are given by-

• a) 0 < a < 4
• b) a > 7
• c) a > 5
• d) a > 0

Answer: 0 < a < 4

Question: The value of the expression x² + 2bx + c will be positive, if-

• a) b² < c
• b) b²–4c < 0
• c) b²–4c > 0
• d) c² < b

Answer: b² < c

Question: If roots of the equation x² + ax + 25 = 0 are in the ratio of 2 : 3 then the value of a is -

• a) ±25/√6
• b) ±5/√6
• c) ±6/√6
• d) None of these

Answer: ±25/√6

Question: If the roots of the equations x² + 3x + 2 = 0 and x² –x +λ=0 are in the same ratio then the value of λ is given by-

• a) 2/9
• b) 7/2
• c) 2/7
• d) 9/2

Answer: 2/9

Question:

• a) a²/ p²
• b) a²/ b²
• c) c²/ r²
• d) None of these

Answer: a²/ p²

Question:

• a) b² pr = q² ac
• b) p² br = a² qc
• c) r² pb = c² ar
• d) None of these

Answer: b² pr = q² ac

Question: The sum of all real roots of the equation |x – 2|2 + | x – 2 | – 2 = 0, is -

• a) 4
• b) 0
• c) 8
• d) None of these

Answer: 4

Question:

• a) None of these
• b)

  

• c)

  

• d)

  

Answer: None of these

Question: If p, q, r are in H.P. and p and r be different having same sign, then the root of the equation px² + 2qx + r = 0 will be

• a) Imaginary
• b) Equal
• c) Real
• d) None of these

Answer: Imaginary

Question: If x = 2 + √3 then the value of x³ – 7x² + 13 x – 12 is –

• a) –9
• b) 9
• c) 6
• d) 3

Answer: –9

Question: If every pair from among the equations x² + px + qr = 0, x² + qx + rp= 0 and x² + rx + pq = 0 has a common root, then the sum of the three common roots is-

• a) p + q + r
• b) pqr
• c) 2 (p + q+ r)
• d) – (p + q + r)

Answer: p + q + r

Question: If the quadratic equations ax² + 2cx + b = 0 and ax² + 2bx + c = 0 (b≠c) have a common root, then a + 4b + 4c is equal to-

• a) 0
• b) –2
• c) –1
• d) 1

Answer: 0

Question: The value of m for which one of the roots of x² – 3x + 2m = 0 is double of one of the roots of x² – x + m = 0 is-

• a) 0, 2
• b) 2, –2
• c) 0, –2
• d) None of these

Answer: 0, 2

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Answer: Statement -1 is False, Statement-2 is True.

Question:

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.