Chapter 9: Q41. (page 595)

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 f^{2} + 7 f - 15 = 0$

Short Answer

Expert verified

Thesolutions of the quadratic equations are $\frac{3}{2}$ androle="math" localid="1647852397706" $- 5$ .

Step by step solution

Step 1. Understand the concept used.

If $a x^{2} + b x + c = 0$ , with $a \neq 0$ , then $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ . Solving using factoring can be done by splitting the middle term of the equation and then making groups and equating them to zero.

Step 2. Substitute the values.

It is given that $2 f^{2} + 7 f - 15 = 0$ . Using the quadratic formula $f = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 2 for $a, 7$ for $b$ and $- 15$ for $c$ .

Put the values in the formula and get $f = \frac{- 7 \pm \sqrt{{(7)}^{2} - 4 \times (2) \times (- 15)}}{2 (2)}$ .

Step 3. Write the solutions.

Simplify the expression for $f$ .

$f = \frac{- 7 \pm \sqrt{{(7)}^{2} - 4 \times (2) \times (- 15)}}{2 (2)}$

$= \frac{- 7 \pm \sqrt{49 + 120}}{4} = \frac{- 7 \pm \sqrt{169}}{4} = \frac{- 7 \pm 13}{4}$

Therefore, either

$f = \frac{- 7 + 13}{4} = \frac{3}{2}$

or,

$f = \frac{- 7 - 13}{4} = - 5$

that is., either $f = \frac{3}{2}$ or $f = - 5$ .

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Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 f^{2} + 7 f - 15 = 0$

Short Answer

Step by step solution

Step 1. Understand the concept used.

Step 2. Substitute the values.

Step 3. Write the solutions.

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Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.2f2+7f−15=0

Short Answer

Step by step solution

Step 1. Understand the concept used.

Step 2. Substitute the values.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 f^{2} + 7 f - 15 = 0$