Question

Which of the following equation has the same root of -5?​

Answer 1

Answer:

⇒ The given quadratic equation is (k+1)x

2

+2(k+3)x+(k+8)=0, comparing it with ax

2

+bx+c=0.

⇒ We get, a=(k+1),b=2(k+3) and c=k+8

⇒ The roots are real and equal.

∴ b

2

−4ac=0

⇒ (2(k+3))

2

−4(k+1)(k+8)=0

⇒ 4(k

2

+6k+9)−4(k

2

+8k+k+8)=0

⇒ 4k

2

+24k+36−4k

2

−36k−32=0

⇒ −12k+4=0

⇒ 12k=4

⇒ k=

12

4

⇒ k=

3

1

∴ The given statement is true.