Question

Find the zeros of the function.

f(x) = 9x^2 + 6x - 8

Answer 1

`\large\boxed{-(4)/(3)\ and\ (2)/(3)}`

Explanation:

`f(x)=9x^2+6x-8\\\\\text{The zeros:}\\\\9x^2+6x-8=0\\\\9x^2+12x-6x-8=0\\\\3x(3x+4)-2(3x+4)=0\\\\(3x+4)(3x-2)=0\iff3x+4=0\ \vee\ 3x-2=0\\\\3x+4=0\qquad\text{subtract 4 from both sides}\\3x=-4\qquad\text{divide both sides by 3}\\\boxed{x=-(4)/(3)}\\\\3x-2=0\qquad\text{add 2 to both sides}\\3x=2\qquad\text{divide both sides by 3}\\\boxed{x=(2)/(3)}`