Free Â Class 10 Relationship between discriminants and nature of roots Worksheets

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Sample Â Class 10 Relationship between discriminants and nature of roots Worksheet Questions

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

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

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

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.

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

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

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.

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.

10.

For what value of K will the equation $(2k + 1)x^{2} + 2(k + 3)x + (k + 5) = 0$ have real and equal roots

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