Question

ax2-kx+81=0 for what value of k the equation has equal rootsx square a x square a x square a x square

Answer 1

Answer:  The answer is $k=\pm\sqrt{324a}.$

Step-by-step explanation:  Given that the following quadratic equation has equal roots.

$ax^2-kx+81=0.$

We need to find the value of 'k' for which the above equation has equal roots. We know that a quadratic equation has equal roots if its discriminant is zero.

Here, discriminant is given by

$D=(-k)^2-4a\times 81=k^2-324a.$

Therefore, for equal roots, we must have

$D=0\\\\\Rightarrow k^2-324a=0\\\\\Rightarrow k^2=324a\\\\\Rightarrow k=\pm\sqrt{324a}.$

Thus, the required value of k is

$k=\pm\sqrt{324a}.$