Question

find k for which the roots of the quadratic equation (k-9)x^2+2 (k-9)x+4=0 equal ​

Answer 1

Given that,

A quadratic equation, $(k-9)x^2+2 (k-9)x+4=0$

To find,

The value of k.

Solution,

If the discriminant of a quadratic equation is equal to 0, then it will have equal roots.

The discriminant of the form of equation, $ax^2+bx+c=0$ is given by :

$D=b^2-4ac=0$

So,

$(2(k-9))^2-4\times (k-9)(4)=0$

$(2(k-9))^2-4\times (k-9)(4)=0\\\\4(k-9)^2-16\times (k-9)=0$

k = 13 and 9

On solving we get the value of k as 13 and 9.