Write a quadratic equation that has zeros at x=2/3 and x=-8

Answer 1

Hi Luisa,

Write a quadratic equation that has zeros at x = 2/3 and x = -8.

In a quadratic equation, an equation can be found from zeros by plugging them into this equation y = (x-a)(x-b), where a and b are the zeros. If you want you can then multiply the terms together to get it in ax^2+bx+c form.

y = (x-2/3)(x+8)

y = x^2 +8x -2/3x - 16/3

y = x^2 + 22/3x - 16/3

Answer 2

(x-2/3)(x+8) = x^2 -(2/3)x + 8x - 2x/3 -16/3 = x^2 - (22/3)x - 16/3 is a quadratic with zeroes 2/3 and -8. Just change the sing of the zeroes, and add x to them. change 2/3 to -2/3 and - 8 to +8, then stick an x in front of them to get two factors. Multiply the 2 factors together. The product is the quadratic polynomial

set it = 0

x^2 - (22/3)x - 16/3 = 0

if you want, multiply by 3 to remove the fractions

3x^3 -22x - 16 =0