Login/Sign Up
Home » Find the nonzero value of for which the roots of the quadratic equation . are real and equal.
Find the nonzero value of \mathrm{k} for which the roots of the quadratic equation 9 x^{2}-3 k x+k=0. are real and equal.
CBSE | Class 10 | Exercise 10D | Maths | Quadratic Equations | RS Aggarwal
Find the nonzero value of \mathrm{k} for which the roots of the quadratic equation 9 x^{2}-3 k x+k=0. are real and equal.

The given equation is 9 x^{2}-3 k x+k=0.

This is of the form a x^{2}+b x+c=0, where a=9, b=-3 k and c=k.

\therefore D=b^{2}-4 a c=(-3 k)^{2}-4 \times 9 \times k=9 k^{2}-36 k

The given equation will have real and equal roots if D=0.

\begin{array}{l} \therefore 9 k^{2}-36 k=0 \\ \Rightarrow 9 k(k-4)=0 \\ \Rightarrow k=0 \text { or } k-4=0 \\ \Rightarrow k=0 \text { or } k=4 \end{array}

But, k \neq 0 (Given)

Hence, the required values of k is 4 .

i

More Material