Question

Form an equation whose roots are cubes of the roots of the equation x ^2+bx+c

Answer 1

Answer:

x²+(2b−a²)x+b²

Step-by-step explanation:

Let α and β be the roots of equation x²+bx+c = 0

Sum of roots: α+β = −a

Product of roots: αβ=b

Let α² and β² be roots of equation x²+Bx+C =0

−A = α²+β² =(α+β)²−2αβ =a2−2b

B = α²β² =(αβ)² =b2

Equation of quadratic equation with roots α² and β²

= x²+(2b−a²)x+b²=0

Thus, the equation whose roots are cubes of the roots of the equation x will be x²+(2b−a²)x+b²=0