Let ​ f(x)=x2+5x−36 ​. Enter the x-intercepts of the quadratic function in the boxes.

Accepted Solution

Answer:[tex]x=-9\text{ or }x=4[/tex]Step-by-step explanation:We have been given a function and we are asked to find the x-intercept of our given function.To find the x-intercepts of our given function we will equate our function formula with 0. [tex]x^2+5x-36=0[/tex]  Now let us factor out our given quadratic equation by splitting the middle term.[tex]x^2+9x-4x-36=0[/tex][tex]x(x+9)-4(x+9)=0[/tex][tex](x+9)(x-4)=0[/tex][tex](x+9)=0\text{ or }(x-4)=0[/tex][tex]x+9-9=0-9\text{ or }x-4+4=0+4[/tex][tex]x=-9\text{ or }x=4[/tex]Therefore, the x-intercepts of our given quadratic functions are [tex]x=-9\text{ or }x=4[/tex].