Question

Prove that for all positive k < 1, the equation (x + a) (x + b) = k (x + c)² has two real
roots, for any real a, b, c.​

Answer 1

Answer:

The quadratic will have real root only when its discriminant will be greater than or equal to 0

Discriminant of given equation =b

2

−4ac =(−8)

2

−4×1×k>0

⇒64−4k>0

⇒4k<64

⇒k<16

So, the value of k should be less than 16.

Answer 2

Answer:

The quadratic will have real root only when its discriminant will be greater than or equal to 0

Discriminant of given equation =b

2

−4ac =(−8)

2

−4×1×k>0

⇒64−4k>0

⇒4k<64

⇒k<16

So, the value of k should be less than 16.