Question

8.For what value of k does the quadratic equation (k-5)X² +2(k-5)x+2=0 have equal roots.​

Answer 1

Answer:

k =7,5

Step-by-step explanation:

The roots of a quadratic equation are equal if and only if b^2-4ac =0

In the given equation, a= (k-5); b =(2k-10); c =2

now, b^2-4ac = (2k-10)^2 - 4×(k-5)×2=0

⇒ 4k^2+100-40k-8k+40=0

⇒4k^2-48k+140 =0

⇒k^2-12k+35=0

⇒k^2-5k-7k+35=0

⇒(k-7)(k-5)=0

⇒k =7,5