Question

1. Find the roots of the quadratic equation
Find the value of k, for which one root of the quadratic equation kx2 - 14x + 8 is six times
the other​

Answer 1

The given equation is

» kx² - 14x + 8 = 0

Divide the equation throughout by k.

» x² - 14x/k + 8/k = 0

Let the two roots be A and 6A.

According to the given condition.

Sum of roots = -b/a

=> A + 6A = 14/k

» 7A = 14/k

» A = 2/k ... (1)

Product of the roots = c/a

=> A × 6A = 8/k

=> 6A² = 8/k ... (2)

Substitute (1) in (2)

» 6 (2/k)² = 8/k

» 6/k² = 8/k

» k = 3/4

Substitute in eq (1)

A = 2/k = (3/4) / 2 = 3/8

6A = 9/4

Therefore, roots are 3/8 and 9/4.