Question

multiple choice 20 points
which equation shows the quadratic formula used correctly to solve 5x² + 3x - 4 = 0 for x?
x = (-3 ± √((3)² + 4(5)(-4)))/(2(5))
x = (3 ± √((3)² - 4(5)(-4)))/(2(5))
x = (-3 ± √((3)² - 4(5)(-4)))/(2(5))
x = (3 ± √((3)² + 4(5)(-4)))/(2(5))

Explanation:

Step1: Recall quadratic formula

For a quadratic equation $ax^{2}+bx + c=0$, the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step2: Identify a, b, c values

In the equation $5x^{2}+3x - 4=0$, $a = 5$, $b=3$, $c=-4$.

Step3: Substitute values into formula

Substitute $a = 5$, $b = 3$, $c=-4$ into the quadratic formula: $x=\frac{-3\pm\sqrt{(3)^{2}-4(5)(-4)}}{2(5)}$.

Answer:

The correct equation is $x=\frac{-3\pm\sqrt{(3)^{2}-4(5)(-4)}}{2(5)}$ (the third - option in the multiple - choice list).