Question

find the value of k if Q.E have two equal and real root 4x²-2(k+1)x+(k+4)=0​

Answer 1

Answer:

As it has real and equal roots, therefore the discriminant is zero.

b

2

−4ac=0

⇒(2(k+1))

2

−4.4(k+1)=0

⇒(2k+2)

2

−16(k+1)=0

⇒4k

2

+8k+4−16k−16=0

⇒4k

2

−8k−12=0

⇒4(k

2

−2k−3)=0

⇒k

2

−2k−3=0

⇒k

2

−3k−k−3=0

⇒k(k−3)+1(k−3)=0

⇒(k−3)(k+1)=0

k−3=0 k+1=0

k=3 k=−1

∴ The roots are 3 and −1.