Question

Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for which Both the roots are greater than 1/2

Answer 1

Answer:

Given,

f(x)=4x

2

−16x+k=0,k∈R

and 1<α<2 and 2<β<3

As a=4>0,

(i) f(1)>0

⇒4−16+k>0

k>12

(ii) f(3)>0

⇒36−48+k>0

k>12

(iii) Discriminant, D>0

⇒256−16k>0

k<16

(iv) f(2)<0

16−32+k<0

⇒k<16

The integral value of k=13,14,15.

The no. of integral values are 3.