Question

If one root is equal to the square of other root of the equation x^2 + x- k = 0,
then k is
​

Answer 1

Answer:

k = 2±√5

Step-by-step explanation:

Let x and y be the roots of the equation.

Then According to question roots of the equation are x and x²

Given,

=> x² + x - k = 0

Now,

=> x² + x = -1 (Sum of roots is -b/a)

=> x² + x + 1 = 0

=> x² + x + 1/4 + 3/4 = 0

=> (x+1/2)² - (√3/2i)² = 0. (i = √-1)

=> (x + 1/2 ± i√3/2) = 0

=> x = -1/2 ± i√3/2...................(1)

Now,

=> x².x = k (Product of roots: c/a)

=> x³ = k

=> k = (-1/2 ± i√3/2)³

=> k = 2±√5