Question

Find the product : 5x²(12^x-4^x2)​

Answer 1

Answer:

The given quadratic equation 5x

2

−4x+2+k(4x

2

−2x−1)=0 can be resolved as:

5x

2

−4x+2+k(4x

2

−2x−1)=0

⇒5x

2

−4x+2+4kx

2

−2kx−k=0

⇒(5+4k)x

2

−(4+2k)x+(2−k)=0

We know that the sum of the roots of a quadratic equation ax

2

+bx+c is −

a

b

and the product of the roots is

a

c

.

Now, in the equation (5+4k)x

2

−(4+2k)x+(2−k)=0, we have:

Product of the roots is:

a

c

=

5+4k

2−k

Also, it is given that the product of the roots is 2, therefore,

5+4k

2−k

=2

⇒2−k=2(5+4k)

⇒2−k=10+8k

⇒−k−8k=10−2

⇒−9k=8

⇒k=−

9

8

Hence, k=−

9

8

.