# How do I determine the x-intercepts of f(x) = -5x² + 20x + 2?

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`f(x)=-5x^2+20x+2`

To determine x-intercept, set f(x)=0.

`0=-5x^2+20x+2`

Then, use the quadratic formula to solve for x.

`x=[-b+-sqrt(b^2-4ac)]/(2a)= [-20+-sqrt((-20)^2-4(-5)(2))]/((-5)(2))= (-20+-2sqrt110)/(-10)`

`x_1= 2+sqrt110/5`                and               `x_2=2-sqrt110/5`

Hence, the x-intercepts of `f(x)=-5x^2+20x+2` are `(2+sqrt110/5,0)` and `(2-sqrt110/5, 0)` .

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