Question

Find the x-intercepts of the function g(x)=8x^{2} −10x−3

Answer 1

Answer: $[-\frac{1}{4}, \frac{3}{2}]$

Step-by-step explanation:

Factor:

• $g(x) = 8x^{2} -10x-3$

• $g(x) = x^{2} -10x-24$ ---> multiply constant (3) by coefficient of first term

• $g(x) = (x+\frac{2}{8})(x-\frac{12}{8} )$ ---> factor (multiplies to 24 and adds to -10. Divide factors by 8 since you multiplied by 8 in previous step)

• $g(x) = (x+\frac{1}{4})(x-\frac{3}{2})$ ---> simplify

• $g(x) = (4x+1)(2x-3)$ ---> move denominator of fraction to be coefficient of x

Solve:

• $0 = (4x+1)(2x-3)$ ---> set equation equal to 0.
• $0 = 4x + 1$ ---> make each parentheses equal to 0.
• $-1 = 4x$
• $-\frac{1}{4} = x$ ---> x intercept
• $0 = 2x - 3$
• $3 = 2x$
• $\frac{3}{2} = x$ ----> x intercept