Question

hi can you help me with this question$y = 2x ^{2} - 7x - 4$Algebraiclly determine the x intercepts of the quadratic equation below.

Answer 1

Step 1: Problem

$y=2x^2\text{ - 7x - 4}$

Step 2: Concept

Use factorization method to determine the values of the x-intercepts

Step 3: Method

x-intercepts occur where y = 0.

$\begin{gathered} 2x^2\text{ - 7x - 4 = 0} \\ 2x^2\text{ - 8x + x - 4 = 0} \\ 2x(\text{ x - 4 ) + 1 ( x - 4) = 0} \\ (\text{ 2x + 1 )( x - 4 ) = 0} \\ 2x\text{ + 1 = 0 or x - 4 = 0} \\ 2x\text{ = -1 or x = 4} \\ x\text{ = }\frac{-1}{2}\text{ or x = 4} \\ x\text{ = - 0.5 or x = 4} \end{gathered}$

x-intercepts = -0.5 and 4

Step 4: Final answer

x-intercepts = -0.5 and 4