Question

a. 0

1. solve using the square root method $4x^2 = 20$

a. $\pm \sqrt{5}$ b. $\pm 10$ c. $\pm 5$

1. solve using the quadratic equation $y = 5x^2 + 11x + 4$

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
a. $x = -.46$ and $x = -1.74$ b. $x = .46$ and $x = 1.74$ c. $x = -.9$ and $x = 3$

Explanation:

Question 31

Step1: Isolate \(x^2\)

Divide both sides of \(4x^2 = 20\) by 4: \(x^2=\frac{20}{4}=5\)

Step2: Apply Square Root

Take square roots of both sides: \(x = \pm\sqrt{5}\)

Step1: Identify \(a\), \(b\), \(c\)

For \(y = 5x^2+11x + 4\), \(a = 5\), \(b = 11\), \(c = 4\)

Step2: Calculate Discriminant

\(b^2 - 4ac = 11^2 - 4\times5\times4 = 121 - 80 = 41\)

Step3: Apply Quadratic Formula

\(x=\frac{-11\pm\sqrt{41}}{2\times5}=\frac{-11\pm6.403}{10}\)

• For \(+\): \(\frac{-11 + 6.403}{10}=\frac{-4.597}{10}\approx - 0.46\)
• For \(-\): \(\frac{-11 - 6.403}{10}=\frac{-17.403}{10}\approx - 1.74\)

Answer:

a. \(\pm\sqrt{5}\)

Question 32