Question

find the equation that formed by each root of x²-x-1=0 is multiplied by 3​

Answer 1

Answer:

x

2

+2x−3=0

x

2

+3x−x−3=0

x(x+3)−1(x+3)=0

(x+3)(x−1)=0

x=−3,1

The roots are squared

So the new roots are (−3)

2

,1

2

=9,1

The quadratic equation with given roots is x

2

−(α+β)x+αβ=0

x

2

−(9+1)x+(9)(1)=0

x

2

−10x+9=0