CBSE Class 10 Mathematics Quadratic Equations MCQs Set C

Question: What is the ratio of the sum and the product of roots of 7x² -12x +18 = 0
a) 7:12
b) 2:3
c) 3:2
d) 7:18
Answer: b

Question: Find the common root of the equations x² - 7x + 10 = 0 and x² - 10x + 16 = 0.
a) - 2
b) 3
c) 5
d) 2
Answer: d

Question: The sides of two square plots are (2x - 1)m and (5x + 4)m . The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot.
a) 15m
b) 13m
c) 31 m
d) 39m
Answer: d

Question: The quadratic equation ax² + bx + c = 0 has no real root. Which of the following is true?
a) b² - 4ac < 0
b) b² - 4ac = 0
c) b² - 4ac > 0
d) b² + 4ac < 0
Answer: a

Question: If the roots of the equation x² + 2cx + ab = 0 are real and unequal, then the equation x² – 2(a + b)x + a² + b² + 2c² = 0 has ________ roots.
a) Real
b) Equal
c) No real
d) Can’t be determined
Answer: c

Question: Which of the following is the quadratic equation one of whose roots is 3 - 2√3 ?
a) x² + 6x - 3 = 0
b) x² - 6x - 3 = 0
c) x² + 6x + 3 = 0
d) x² - 6x + 3 = 0
Answer: b

Question: If the roots of the equation (a² + b²) x² – 2b(a + c)x + (b² + c²) = 0 are equal, then ________.
a) 2b = a + c
b) b² = ac
c) b = 2ac/a+b
d) b = ac
Answer: b

Question: If the roots of x² + 4mx + 4m² + m + 1 = 0 are real, which of the following is true?
a) m = - 1
b) m ≤ - 1
c) m ≥ -1
d) m ≥ 0
Answer: b

Question: If the equation ax - 5x + c = 0 has 10 as the sum of the roots and also as the product of the roots, which of the following is true?
a) a - c = 5
b) a = 2,c = 3
c) a = 5, c =1
d) a = 3, c = 2
Answer: a

Question: If the product of the roots of x² - 3x + k = 10 is - 2, what is the value of' k'?
a) -2
b) 8
c) 12
d)-8
Answer: b

Question: What is the ratio of the sum and the product of roots of 7x² - 12x + 18 = 0
a) 7:12
b) 2:3
c) 3:2
d) 7:18
Answer: b

Question: In the equation

the roots are equal when m = __.

a) 1/2
b) − 1/2
c) 0
d) 1
Answer: b

Question: Read the statement carefully and state ‘T’ for true and ‘F’ for false

(ii) A line segment AB of length 2 m is divided at C into two parts such that AC² = AB·CB. The length of the part CB is 3 + √5 .
(iii) Every quadratic equation can have at most two real roots.
(iv) A real number a is said to be root of the quadratic equation ax² + bx + c = 0, if aα² + bα + c = 0.
(i) (ii) (iii) (iv)
a) F T T T
b) F T T F
c) T F F T
d) F F T T
Answer: d

DIRECTIONS : Study the given Case/Passage and answer the following questions

Case/Passage-I

Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.

Question: What will be the distance covered by Ajay’s car in two hours?
(a) 2(x +5)km
(b) (x – 5)km
(c) 2( x + 10)km
(d) (2x + 5)km

Answer: a

Question: Which of the following quadratic equation describe the speed of Raj’s car?
(a) x² – 5 x – 500 = 0
(b) x² + 4x - 400 = 0
(c) x² + 5x – 500 = 0
(d) x² – 4x + 400 = 0

Answer: c

Question: What is the speed of Raj’s car?
(a) 20 km/hour
(b) 15 km/hour
(c) 25 km/hour
(d) 10 km/hour

Answer: a

Question: How much time took Ajay to travel 400 km?
(a) 20 hour
(b) 40 hour
(c) 25 hour
(d) 16 hour

Answer: d

Case/Passage-II

The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more for upstream than downstream.

Question: Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be
(a) 20 km/hr
(b) (20 + x) km/hr
(c) (20 - x) km/hr
(d) 2 km/hr

Answer: c

Question: What is the relation between speed ,distance and time?
(a) speed = (distance )/time
(b) distance = (speed )/time
(c) time = speed x distance
(d) speed = distance x time

Answer: a

Question: Which is the correct quadratic equation for the speed of the current ?
(a)x² + 30x − 200 = 0
(b) x² + 20x − 400 = 0
(c) x² + 30x − 400 = 0
(d) x² − 20x − 400 = 0

Answer: a

Question: What is the speed of current ?
(a) 20 km/hour
(b) 10 km/hour
(c) 15 km/hour
(d) 25 km/hour

Answer: a

Question: How much time boat took in downstream?
(a) 90 minute
(b) 15 minute
(c) 30 minute
(d) 45 minute

Answer: c

True / False

DIRECTIONS : Read the following statements and write your answer as true or false.

Question: A quadratic equation cannot be solved by the method of completing the square. 
Answer: False

Question: (x² + 3x + 1) = (x – 2)² is not a quadratic equation.
Answer: True

Question: If sum of the roots is 2 and product is 5, then the quadratic equation is x² – 2x + 5 = 0
Answer: True

Question: Sum of the reciprocals of the roots of the equation x² + px + q = 0 is 1/p.
Answer: False

Question: If we can factorise ax² + bx + c, a ≠ 0, into a product of two linear factors, then the roots of the quadratic equation ax² + bx + c = 0 can be found by equating each factor to zero. (x – 2) (x + 1) = (x – 1) (x + 3) is a quadratic equation.
Answer: False

Question: The nature of roots of equation x² + 2x√3 + 3 = 0 are real and equal.
Answer: True

Question: x² + x – 306 = 0 represent quadratic equation where product of two consecutive positive integer is 306.
Answer: True

Question: The roots of the equation (x – 3)² = 3 are 3 ±√3
Answer: True

Question: For the expression ax² + 7x + 2 to be quadratic, the possible values of a are non-zero real numbers.
Answer: True

Question: Read the statements carefully.
Statement - I : The quadratic equation ax² + bx + c = 0 has two distinct real roots, if b² – 4ac ≥ 0.
Statement - II : The quadratic equation 2(a² + b2)x² + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
a) Both Statement - I and Statement - II are true.
b) Statement - I is true but Statement - II is false.
c) Statement - I is false but Statement - II is true.
d) Both Statement - I and Statement - II are false.
Answer: c

One Word Questions :

Question: Find the roots of the equation y2 + 1/2 , y - 1 = 0 .
Answer: -1 + √7/4 , - 1 - √7/4

Question: What are the two value of z which satisfy the equation z² + 2z – 8 = 0?
Answer: – 4, 2

Question: Difference of the natural number and its reciprocal is 3/2 . What is the number?
Answer: 2

Question: Find the value of discriminant of the equation √3x² – 2 √2x – 2 √3 =0
Answer: 32

 Question: What value of x will satisfy the equation x² = (x + 5)(x + 3)?
Answer: -15/8

Question: Find the roots of the equation 3x²+2 5x – √5=0 .
Answer: - √5 , √5/3

 Question: Solve the quadratic equation : ax² – 2abx = 0.
Answer: x = 0 or x = 2b

Question: What are the two roots of the equation (x + 4) (x – 5) = 0?
Answer: – 4, 5

Question: For what value of p the equation px² + 4x + 1 = 0 will have equal roots?
Answer: 4

 Question: If –4 is a root of the equation x² + px – 4 = 0 and the quadratic equation x² + px + k = 0 has equal roots, find the value of k.
Answer: 9/4

Question: The product of Ramu’s age (in years) five years ago and his age (in years) nine years later is 15. Determine Ramu’s present age.
Answer: 6 years

 Question: One root of the quadratic equation 2x² 3x k 0 is 1/2. What is the value of k?
Answer: –2

Question: What is the solution set of equation 3x² + 5x – 2 = 0?
Answer: {1/3 , -2}

Question: What are the two roots of the equation (x + 5)² – 36 = 0?
Answer: 1, –11

Question: Find the solutions of quadratic equation : y²+2 √3y+3= 0 .
Answer: y = – √3, – √3

Question: What are the value of p and q if these are the roots of the equation x² + px + q = 0?
Answer: p = 1, q = –2

Question: Find the value of discriminant in 25x² – 30x + 9 = 0.
Answer: 0

Question: If sum of a whole number and its reciprocal is 17/4 , what is the number?
Answer: 4

Question: The length of a hall is 10m more than its breadth. Find the length and breadth of the hall if its area is 600m².
Answer: 30m, 20m

Question: The sum S of n successive odd natural numbers starting from 3 is given by the relation S = n(n + 2). Determine n, if the sum is 168.
Answer: n = 12

Question: If one root of the quadratic equation x² mx –16 0 is negetive of other then what is the value of m?
Answer: 0

Question: One side of the rectangle exceeds the other side by 3cm. If the area of rectangle is 180sq.cm., find the two sides of the rectangle.
Answer: 12cm, 15cm

Question: The quadratic equation ax² + bx + c has equal roots. What are the roots?
Answer: - b/a

Question: What is the equation whose roots are 2+ √3 and 2 – √3 ?
Answer: x² – 4x + 1 = 0

Question: If , are the roots of the equation 3x² 7x 3 0 , then what is the value of .
Answer: - 4/3