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CBSE Class 10 Mathematics Worksheet

UNIT II: Algebra - Quadratic Equations

Find the value of k for which the quadratic equation $(k - 2)x^{2} + 2(2k - 3) + (5k - 6) = 0$ has equal roots

Find the roots of the equation $2x^{2} + x - 4 = 0$ by the method of completing the squares.

If the quadratic equation $(1 + a^{2})b^{2}x^{2} + 2abcx + (c^{2} - m^{2}) = 0$ , in x has equal roots, prove that $c^{2} = m^{2}(1 + a^{2})$

If roots of the equation $x^{2} + 2px + mn = 0$ are equal show that the roots of the equation $x^{2} - 2(m + n)x + (m^{2} + n^{2} + 2p^{2}) = 0$ are also equal.

If the roots of the quadratic equation $(b - c)x^{2} + (c - a)x + (a - b) = 0$ are equal prove that 2b = a + c

If 2 is the root of the equation $x^{2} + kx + 12 = 0$ and the equation $x^{2} + kx + q = 0$ has equal roots, find the value of q

Find the positive value of K for which equation $x^{2} + kx + 64 = 0$ and $x^{2} - 8x + k = 0$ both will have equal roots.

Find the value of k for which the equation $(3k + 1)x^{2} + 2(k + 1)x + 1$ has equal roots. Also find the roots.

Find the value of K for which the quadratic equation $9x^{2} - 3kx + k = 0$ has equal roots

10.

Find the value of P for which the quadratic equation $(p + 1)x^{2} - 6(p - 1)x + 3(p + 9) = 0, p \neq -1$ has equal roots.

11.

For what value of k, the roots of the quadratic equation $kx(x - 2\sqrt{5}) + 10 = 0$ are equal

12.

Find the value of P for which the quadratic equation $4x^{2} - px + 3 = 0$ has equal roots

13.

Find the nature of the roots of the quadratic equation $13\sqrt{3}x^{2} + 10x\sqrt{3} = 0$

14.

Find | $x^{2}$ |value if

⁼⁰

2.999

3.999

4.38

2.105

15.

If x = -2 is a root of the equation $3x^{2} + 7x + p = 0$ , find the value of k so that the roots of the equation $x^{2} + k(4x + k - 1) + p = 0$ are equal.

16.

Find what value of k, the roots of quadratic equation $kx^{2} + 4x + 1 = 0$ are real and equal

17.

If the roots of the quadratic equation $(a - b)x^{2} + (b - c)x + (c - a) = 0$ are equal, prove that 2a = b + c

18.

Determine the positive value of k for which the equation $x^{2} + kx + 64 = 0$ and $x^{2} - 8x + k = 0$ will both have real and equal roots

19.

20.

Find the positive value of K for which equation $x^{2} - 8x + k = 0$ will have equal roots.

CBSE Class 10 Mathematics Worksheet

UNIT II: Algebra - Quadratic Equations

Answers

k = 1, 3

Roots are $x = -1/\sqrt{33}/4$ , $-1 - \sqrt{33}/4$

$c^{2} = m^{2}(1 + a^{2})$ , Proved

Yes both are equal

2b = a + c, proved

q = 16

k = 16 for both the equation

k = 0, 1; x = -1/2

k = 4

10.

p = -1, 3

11.

k = 2

12.

$4\sqrt{3}, -4\sqrt{3}$

13.

-56 so the equation is not real root

14.

Option A

15.

k = 2/3, -1

16.

k = 4

17.

To be proved

18.

For equation I0 k = ± 16, ii) 16

19.

Option D

20.

k = 16

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