Question

10. If one root of the equation 3x2 +kx -81 = 0 is the square of the other, find k.

Answer 1

Let one root of given equation is r
Then other root of given equation is r²

Now, product of roots = r.r² = r³ = constant/coefficient of x²
r³ = 27 = 3³
⇒ r = 3

Now, sum of roots = r + r² =- coefficient of x/coefficient of x² = - k/3
3 + 3² = - k/3
⇒12 × 3 = -k
⇒k = -36

Answer 2

HELLO DEAR,

Let one root be x
and other root be x²

Now,

product of roots = x*x² = (b/a)

x³ = 27/1

r³ = 3³

r = 3

Now,

sum of roots = r + r² = -(b/a)

3 + 3² = - k/3

3 + 3² = - k/3

12 × 3 = -k

k = -36



I HOPE ITS HELP YOU DEAR,
THANKS