Chapter 9: Q. 130 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$2 x^{2} - x + 1 = 0$

Short Answer

Expert verified

The solutions of the given equation are $x = \frac{1}{4} \pm \frac{\sqrt{7}}{4} i$ .

Step by step solution

Step 1. Given information.

The given equation is:

$2 x^{2} - x + 1 = 0$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a x^{2} + b x + c = 0$ is:

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

In the given equation, $a = 2, b = - 1, c = 1$ . Substitute these values in Quadratic Formula.

$x = \frac{- (- 1) \pm \sqrt{(- 1)^{2} - 4 (2) (1)}}{2 (2)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} x & = & \frac{1 \pm \sqrt{1 - 8}}{4} \\ x & = & \frac{1 \pm \sqrt{- 7}}{4} \\ x & = & \frac{1}{4} \pm \frac{\sqrt{- 7}}{4} \\ x & = & \frac{1}{4} \pm \frac{\sqrt{7}}{4} i [∵ \sqrt{- 1} = i] \end{array}$

Step 4. Conclusion.

The solutions of the given equation are $x = \frac{1}{4} \pm \frac{\sqrt{7}}{4} i$ .

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In the following exercises, solve by using the Quadratic Formula.
$2 x^{2} - x + 1 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values in Quadratic Formula.

Step 3. Simplify the value.

Step 4. Conclusion.

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In the following exercises, solve by using the Quadratic Formula.2x2-x+1=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values in Quadratic Formula.

Step 3. Simplify the value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Calculus

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using the Quadratic Formula.
$2 x^{2} - x + 1 = 0$