Question

Question #a01c5

Answer 1

The value of `k` is `=84`

Explanation:

For a perfect square, the discriminant `Delta=0`

for the quadratic equation

`ax^2+bx+c=0`

Here, we have

`4x^2-32x-20+k=0`

The discriminant is

`Delta=b^2-4ac=32^2-4*4*(k-20)`

`32^2-16k+320=0`

`16k=1344`

`k=1344/16=84`

So, the equation becomes

`4x^2-32x-20+84=0`

`4x^2-32x+64=0`

`4(x^2-8x+16)=0`

`4(x-4)^2=0`

`(2(x-4))^2=0`