Question

Construct a quadratic equation using the following roots

Answer 1

1) 63x²+68x+12=0

2) x⁴-8x²+15=0

3) -5x²-(5/x²)+26=0

Explanation:

1)

x=-6/7 and x=-2/9

7x=-6 and 9x=-2

7x+6=0 and 9x+2=0

(7x+6)(9x+2)

63x²+14x+54x+12

63x²+68x+12=0

2)

x=√3 and x=√5

x²=3 and x²=5

x²-3=0 and x²-5=0

(x²-3)(x²-5)

x⁴-5x²-3x²+15

x⁴-8x²+15=0

3)

x=
`\sqrt[2]{5}` and x=
`\sqrt[-2]{5}`

x²=5 and x⁻²=5

x²=5 and (1/x²)=5

x²-5=0 and (1/x²)-5=0

(x²-5)((1/x²)-5)

1-5x²-(5/x²)+25

-5x²-(5/x²)+26=0