Question

If the roots of the quadratic equation (k-5) x² + 2 (k-5) x + 2 = 0 are real and equal, find the value/s of k.​

Answer 1

Answer:

The quadratic equation (k-5)x2 + 2(k-5)x + 2 =0 have equal roots. ⇒ k = 7 or 5.

Answer 2

Step-by-step explanation:

SOLUTION

The given quadratic equation is (k-5)x^2+2(k-5)x+2=0

Theory

For the roots to be equal, the discriminant (D) b^2-4ac should be equal to zero

Procedure

Now, b^2-4ac=0

==>4(k-5)^2- 4(k-5) =0

==>4(k^2+25-10k) - (4k-20) =0

==>4k^2-40k+100-4k+20=0

==>4k^2-44k+120=0

==>k^2-11k+30=0

==>k =5,6