Question

Find the value of k, for which one root of the quadratic equation kx^2+14^+8=0 is six times the other.

Answer 1

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Here's your answer...

Let one root be y.

Then the other root must be 6y.

In a quadratic equation of form ax²+bx+c = 0, the product of its roots = c/a and the sum of roots is -b/a.

In the equation kx²+14x+8 = 0, the product of roots is 8/k and sum of roots is -14/k

8/k = 6y×y
8/k = 6y²
4/k = 3y²

-14/k = 6y+y
-14/k = 7y
y = -2/k

Putting y's value in the product of roots...
4/k = 3×(-2/k)²
4/k = 12/k²
k²/k = 12/4
k = 3

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