# 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

1.

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

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

8.

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

9.

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

10.

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

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