Chapter 7: Q. 1 (page 505)

Find the real solutions, if any, of the equation $3 x^{2} + x - 1 = 0$ .

Short Answer

Expert verified

The solutions are $\{\frac{- 1 - \sqrt{13}}{6}, \frac{- 1 + \sqrt{13}}{6}\}$ .

Step by step solution

Step 1. Given Information

We are given the equation $3 x^{2} + x - 1 = 0$ and we need to find the real roots of it.

Step 2. Finding the discriminant

The standard form of a quadratic equation is $a x^{2} + b x + c = 0$ .

Comparing it with the given equation we get,

$a = 3, b = 1, c = - 1$ .

Discriminant of the equation is

role="math" localid="1646502307564" $b^{2} - 4 a c = {(1)}^{2} - 4 (3) (- 1) = 1 + 12 = 13 > 0$

Thus there are two unequal real solutions for $x$ .

Step 3. Finding the roots

Using the quadratic formula to find the roots:

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Substituting the values we get,

role="math" localid="1646502325187" $x = \frac{- 1 \pm \sqrt{1^{2} - 4 (3) (- 1)}}{2 (3)} \Rightarrow x = \frac{- 1 \pm \sqrt{1 + 12}}{6} \Rightarrow x = \frac{- 1 \pm \sqrt{13}}{6} \Rightarrow x = \frac{- 1 - \sqrt{13}}{6}, \frac{- 1 + \sqrt{13}}{6}$

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Find the real solutions, if any, of the equation $3 x^{2} + x - 1 = 0$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the discriminant

Step 3. Finding the roots

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Find the real solutions, if any, of the equation3x2+x-1=0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the discriminant

Step 3. Finding the roots

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Find the real solutions, if any, of the equation $3 x^{2} + x - 1 = 0$ .