Question

Given that the equation (k + 1)x² - 4x +9 = 0 has two different roots. Determine the range of values of k.​

Answer 1

Answer:

The given equation is,

x

2

+k(4x+k−1)+2=0⇒x

2

+4kx+k(k−1)+2=0

Here, a=1,b=4k,c=k(k−1)+2=0

∴D=b

2

−4ac=(4k)

2

−4×1[k(k−1)+2]=16k

2

−4k(k−1)−8

⇒D=16k

2

−4k

2

+4k−8

⇒D=12k

2

+4k−8⇒D=4(3k

2

+k−2)

⇒D=4[3k(k+1)−2(k+1)]⇒D=4(3k−2)(k+1)

The given equation will have equal roots, if

D=0⇒4(3k−2)(k+1)=0⇒k=

3

2

ork=−1