Question

What is the sum of the x-intercepts of the function j(x) = 6x2 + 7x - 5?

Answer 1

The given function is-

`j(x)=6x^2+7x-5`

Let's use the quadratic formula

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where a = 6, b = 7, and c = -5.

`\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4\cdot6\cdot(-5)}}{2\cdot6}=\frac{-7\pm\sqrt[]{49+120}}{12} \\ x=\frac{-7\pm\sqrt[]{169}}{12}=(-7\pm13)/(12) \\ x_1=(-7+13)/(12)=(6)/(12)=(1)/(2) \\ x_2=(-7-13)/(12)=(-20)/(12)=-(5)/(3) \end{gathered}`

Then, we add these solutions

`(1)/(2)-(5)/(3)=(1\cdot3-5\cdot2)/(2\cdot3)=(3-10)/(6)=(-7)/(6)`

Hence, the answer is -7/6.