Question

If the quadratic equation x^2-kx+k+1=0 may have roots in the ratio of 2:3 find the value of k.​

Answer 1

Answer:

Let α be the common root.

Then kα

2

+α+k=0 and kα

2

+kα+1=0

Solving, we get

1−k

2

α

2

=

k

2

−k

α

=

k

2

−k

1

⇒

k

2

−k

1−k

2

=

k

2

−k

k

2

−k

=1

⇒2k

2

−k−1=0⇒k=−

2

1

,1

For k=1, equations become identical, thus not possible.

Hence, k=−

2

1

.

Hope it helps!