Question

If the roots of x²+kx+k+3=0 are real and equal, what is the value of k?​

Answer 1

Answer:

Values of k are 0 and 4.

Step-by-step explanation:

Given that roots of x^2 + kx + k = 0x

2

+kx+k=0 are real and equal. we have to find the value of k.

The general form of quadratic equation is

ax^2+bx+cax

2

+bx+c

Compare above with given equationx^2 + kx + k = 0x

2

+kx+k=0 , we get

a=1, b=k, c=k

As the roots of given equation are equal

⇒ Discriminant is 0.

i.e b^2-4ac=0b

2

−4ac=0

⇒ k^2-4k=0k

2

−4k=0

⇒ k(k-4)=0k(k−4)=0

⇒ k=0, 4k=0,4

hence, values of k are 0 and 4