Find the quadratic equation given the solutions.

Question

1) x = 9 , x = -5

2) x = 3i , x = -3i

3) x = square root of 3 , x = negative sq rt of 3

Answer 1

x=9, x=-5

(x-9)(x+5) = x^2 -4x -45 = 0 or f(x) = x^2-4x -45

x=3i, x=-3i

(x-3i)(x+3i) = x^2+3 = 0 or f(x) =x^2+3

x=sqr3 x=-sqr3

(x-sqr3)(x+sqr3) = x^2 -3 = 0 or f(x) =x^2+3

just take each x value, change it's sign, stick an x in front of it, that gives you the factors. Multiply them together to get the quadratic polynomial. Set it equal to zero, or equal to f(x) or to y.