Chapter 9: Q.123 (page 898)

In the following exercises, solve by using the Quadratic Formula: $2 a^{2} - 6 a + 3 = 0$

Short Answer

Expert verified

The solution of the quadratic equation is $a = \frac{3 \pm \sqrt{3}}{2}$

Step by step solution

Given information

We are given a quadratic equation $2 a^{2} - 6 a + 3 = 0$

Identify the values of x,y,z

On comparing with standard equation we get $x = 2, y = - 6, z = 3$

Write the quadratic formula and substitute the values in it

The quadratic formula can be given as

$a = \frac{- y \pm \sqrt{y^{2} - 4 x z}}{2 x}$

On substituting the values we get

$a = \frac{6 \pm \sqrt{36 - 4 (2) (3)}}{2 (2)}$

Simplify

On simplifying we get,

$a = \frac{6 \pm \sqrt{36 - 24}}{4} a = \frac{6 \pm \sqrt{12}}{4} a = \frac{6 \pm 2 \sqrt{3}}{4}$

Take out and remove the common factor

We get

$a = \frac{2 (3 \pm \sqrt{3})}{4} a = \frac{3 \pm \sqrt{3}}{2}$

Conclusion

The solution of the quadratic equation of $a = \frac{3 \pm \sqrt{3}}{2}$

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In the following exercises, solve by using the Quadratic Formula: $2 a^{2} - 6 a + 3 = 0$

Short Answer

Step by step solution

Given information

Identify the values of x,y,z

Write the quadratic formula and substitute the values in it

Simplify

Take out and remove the common factor

Conclusion

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In the following exercises, solve by using the Quadratic Formula:2a2-6a+3=0

Short Answer

Step by step solution

Given information

Identify the values of x,y,z

Write the quadratic formula and substitute the values in it

Simplify

Take out and remove the common factor

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using the Quadratic Formula: $2 a^{2} - 6 a + 3 = 0$