Question

what value of m for which two roots of the quadratic equation 4x^2+4(3m-1)x+(m+7)=0 are reciprocal to each other.

Answer 1

The value of m is (- 3).

Step-by-step explanation:

The given quadratic equation is

4x² + 4 (3m - 1)x + (m + 7) = 0 ..... (1)

Let p, 1/p are the roots of (1). Then using the relation between roots and coefficients, we get

p + 1/p = - 4 (3m - 1)/4 ..... (2)

p * 1/p = (m + 7)/4

or, 1 = (m + 7)/4

or, m + 7 = 4

or, m = - 3

Therefore the value of m is (- 3).

Check:

When m = - 3, from (1), we get

4x² - 40x + 4 = 0

or, x² - 10x + 1 = 0

Using the quadratic formula, we get

x = [- (- 10) ± √{(- 10)² - (4 * 1 * 1)}]/(2 * 1)

= {10 ± √(100 - 4)}/2

= (10 ± 2√24)/2

= 5 ± √24

So the roots are 5 + √24 and 5 - √24

Now (5 + √24) (5 - √25)

= 25 - 24

= 1

Hence the roots are reciprocal to each other.

Thus verified.