Question

Find the x-intercept(s) of y = 2x2 - 3x - 5.

A) -5
B) 2 1/2, -1
C) 3, -5
D) 5, -1

Answer 1

`\large\boxed{B)\ 2(1)/(2),\ -1}`

Explanation:

x-intercepts are for y = 0.

We have the equation:

`y=2x^2-3x-5`

Therefore

`2x^2-3x-5=0\\\\2x^2+2x-5x-5=0\\\\2x(x+1)-5(x+1)=0\\\\(x+1)(2x-5)+0\iff x+1=0\ \vee\ 2x-5=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\\boxed{x=-1}\\\\2x-5=0\qquad\text{add 5 to both sides}\\2x=5\qquad\text{divide both sides by 2}\\\boxed{x=2(1)/(2)}`