Chapter 10: Q 102 (page 1195)

Solve the equation using quadratic formula.
$3 q^{2} + 8 q - 3 = 0$

Short Answer

Expert verified

The roots are $q = - 3, q = \frac{1}{3}$ .

Step by step solution

Given Information.

The given equation is $3 q^{2} + 8 q - 3 = 0$ .

Write the quadratic equation in standard form and identify a,b,c.

The quadratic equation is in standard form.

So,

$a = 3, b = 8, c = - 3$

Substitute the values in quadratic formula.

$q = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} q = \frac{- (8) \pm \sqrt{(8)^{2} - 4 (3) (- 3)}}{2 (3)} q = \frac{- 8 \pm \sqrt{64 + 36}}{6} q = \frac{- 8 \pm \sqrt{100}}{6}$

Use the square root property.

$q = \frac{- 8 \pm 10}{6}$

Rewrite to show two solutions.

$q_{1} = \frac{- 8 + 10}{6} q_{1} = \frac{2}{6} q_{1} = \frac{1}{3}, q_{2} = \frac{- 8 - 10}{6} q_{2} = \frac{- 18}{6} q_{2} = - 3$

Thus, the solutions are $q = - 3, q = \frac{1}{3}$ .

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Solve the equation using quadratic formula.
$3 q^{2} + 8 q - 3 = 0$

Short Answer

Step by step solution

Given Information.

Write the quadratic equation in standard form and identify a,b,c.

Substitute the values in quadratic formula.

Rewrite to show two solutions.

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Solve the equation using quadratic formula.3q2+8q-3=0

Short Answer

Step by step solution

Given Information.

Write the quadratic equation in standard form and identify a,b,c.

Substitute the values in quadratic formula.

Rewrite to show two solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Calculus

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Solve the equation using quadratic formula.
$3 q^{2} + 8 q - 3 = 0$