Question

question 5 of 10
find the solutions to the equation below.
check all that apply.
2x² + 11x + 5 = 0
a. x = -5
b. x = 3
c. x = 4
d. x = -1/2
e. x = -3
f. x = 2

Explanation:

Step1: Factor the quadratic equation

For the quadratic equation \(2x^{2}+11x + 5=0\), we need to find two numbers that multiply to \(2\times5 = 10\) and add up to \(11\). The numbers are \(10\) and \(1\). So we can rewrite the middle - term: \(2x^{2}+10x+x + 5=0\). Then factor by grouping: \(2x(x + 5)+1(x + 5)=0\), which gives \((2x + 1)(x+5)=0\).

Step2: Solve for \(x\) using the zero - product property

If \((2x + 1)(x + 5)=0\), then either \(2x+1 = 0\) or \(x + 5=0\).
If \(2x+1=0\), then \(2x=-1\), and \(x=-\frac{1}{2}\).
If \(x + 5=0\), then \(x=-5\).

Answer:

A. \(x=-5\), D. \(x =-\frac{1}{2}\)