Question

If roots of ax^2+bx+c=0 are alpha and beta then whose equation roots are alpha square and beta square

Answer 1

Answer:

a²x²-(b²-2ac)x+c²=0

Step-by-step explanation:

roots of ax^2+bx+c=0 are  α and β

So αβ=c/a and α+β=-b/a

The equation with roots α² and β² will be

x²-( α² + β² )x+α²β² =0

x²-{( α + β)² -2αβ}x+(αβ)²=0

x²-{ (-b/a)²-2c/a) }x+ (c/a)²=0

x²- { b²/a²-2c/a)}x +c²/a²=0

x²--( b²-2ac)/a²*x +c²/a²=0

Multiplying by a² we get

a²x²-(b²-2ac)x+c²=0