Question

find k so that the quadratic equation has equal roots ... (k-4)x^2 + 2(k-4)X+4​

Answer 1

ANSWER:-

Given:

Quadratic equation has equal roots are;

(k-4)x² + 2(k-4)x +4=0.

To find:

Find the value of k.

Solution:

The roots of the quadratic equation;

=) Ax² +Bx + C= 0

We know that, D= b² -4ac is called discriminant.

D=0

Therefore,

⏺️A= k-4

⏺️B=2(k-4)= 2k-8

⏺️C= 4

So,

b² - 4ac =0

=) (2k-8)² - 4×k-4× 4=0

=) (2k-8)² - 4k×-16=0

=) (2k)² +(8)² -2×2k×8 + 64k=0

=) 4k² + 64 -32k +64k=0

=) 4k² + 64 + 32k =0

=) 4k² +32k+64=0

=) k² + 8k + 16=0

=) k² +4k+4k +16=0

=) k(k+4) +4(k+4)=0

=) (k+4) (k+4)=0

=) k+4 =0 OR k+4=0

=) k= -4 OR k= -4

Hope it helps ☺️