CBSE Class 10 Mathematics Quadratic Equations Assignment Set 20

Question. Check whether the following equations
(i) \( x(x+1) + 9 = (x+2)(x-3) \)
(ii) \( x(2x-3) - 1 = x^2 + 5x \)
are quadratic?
Answer: (i) NO (ii) Yes

Question. For the quadratic equation \( x^2 + \sqrt{2}x - 4 = 0 \), is \( x = -2\sqrt{2} \), a solution?
Answer: Yes

Question. If \( x=2 \) is a solution of \( 3x^2 - 2px + 5 = 0 \), find the value of \( p \).
Answer: \( p = \frac{17}{4} \)

Question. Solve the quadratic equation \( 6x^2 - 5x + 1 = 0 \) for \( x \).
Answer: \( \frac{1}{2}, \frac{1}{3} \)

Question. If \( x=2 \) and \( x=3 \) are the two solutions of the equation \( 3x^2 - 2px + 2q = 0 \). Find the value of \( p, q \).
Answer: \( p = \frac{15}{2}, q = 9 \)

Question. Solve the following quadratic equations
(i) \( (x+5)(x-5) = 39 \)
(ii) \( \frac{x+1}{x-1} + \frac{x-1}{x+1} = \frac{10}{3} \)
Answer: (i) \( x = \pm 8 \) (ii) \( x = \pm 2 \)

Question. Is 3 a root of the following equation?
\( \sqrt{x^2 - 4x + 3} + \sqrt{x^2 - 9} = \sqrt{4x^2 - 14x + 16} \)
Answer: No

Question. The sum of a number and its reciprocal is \( \frac{13}{6} \). Find the numbers.
Answer: \( \frac{3}{2}, \frac{2}{3} \)

Question. Write a quadratic equation and solve it, "The square of a number exceeds the number by 20".
Answer: \( x^2 - x = 20 \), solution is \( 5, -4 \)

Question. By factorising, find the solution of the following equations
(i) \( 2\sqrt{2}x^2 + 4x + \sqrt{2} = 0 \)
(ii) \( x^2 + 4\sqrt{2}x + 6 = 0 \)
Answer: (i) \( \left(-\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}}\right) \) (ii) \( (-3\sqrt{2}, -\sqrt{2}) \)

Question. Find two numbers whose sum is 27 and product is 182.
Answer: 13 and 14

Question. The altitude of a right triangle is \( 7\text{ cm} \) less than its base. If the hypotenuse is \( 13\text{ cm} \), find the other two sides.
Answer: \( 5\text{ cm} \) and \( 12\text{ cm} \)