Question

homework 9: section 2.5
score: 150/280 answered: 15/28
question 18
solve the equation by using the quadratic formula
$2p^2 + p - 4 = 0$
simplify answers. list multiple answers with a comma in between.
question help: video message instructor

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 2\), \(b = 1\), \(c = -4\).

Step2: Quadratic formula

Quadratic formula: \(p=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute \(a = 2\), \(b = 1\), \(c = -4\) into formula:
\(p=\frac{-1\pm\sqrt{1^2 - 4\times2\times(-4)}}{2\times2}\)

Step3: Calculate discriminant

Calculate discriminant: \(1^2 - 4\times2\times(-4)=1 + 32 = 33\)

Step4: Solve for p

\(p=\frac{-1\pm\sqrt{33}}{4}\)

Answer:

\(\frac{-1 + \sqrt{33}}{4},\frac{-1 - \sqrt{33}}{4}\)