Chapter 9: Q. 9.42 (page 889)

Solve by using the Quadratic Formula: $4 z^{2} + 2 z - 6 = 0$

Short Answer

Expert verified

The roots of the above equation is $z = 1$ and $z = - \frac{3}{2}$

Step by step solution

Given information

We are given a quadratic equation $4 z^{2} + 2 z - 6 = 0$

Step 2: Identify the values of a,b,c

On comparing with standard form we get the values of $a, b, c$ as $a = 4, b = 2, c = - 6$

Write the quadratic equation formula and substitute the values of a,b,c and then simplify and solve for x

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

Substituting the values we get

$z = \frac{- 2 \pm \sqrt{4 - 4 (4) (- 6)}}{2 (4)} z = \frac{- 2 \pm \sqrt{4 + 96}}{8} z = \frac{- 2 \pm \sqrt{100}}{8} z = \frac{- 2 \pm 10}{8}$

On further simplifying we get

$z = \frac{- 2 + 10}{8} z = \frac{8}{8} z = 1$ and $z = \frac{- 2 - 10}{8} z = \frac{- 12}{8} z = - \frac{3}{2}$

Step 4: check the solutions

We substitute $x = 1$ in the quadratic equation

$4 z^{2} + 2 z - 6 4 {(1)}^{2} + 2 (1) - 6 4 + 2 - 6 = 0$

Now we substitute $z = - \frac{3}{2}$ in the above equation

$4 z^{2} + 2 z - 6 4 {(- \frac{3}{2})}^{2} + 2 (- \frac{3}{2}) - 6 9 - 3 - 6 = 0$

Conclusion

The solution of the above equation is $z = 1$ and $z = - \frac{3}{2}$

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Solve by using the Quadratic Formula: $4 z^{2} + 2 z - 6 = 0$

Short Answer

Step by step solution

Given information

Step 2: Identify the values of a,b,c

Write the quadratic equation formula and substitute the values of a,b,c and then simplify and solve for x

Step 4: check the solutions

Conclusion

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Solve by using the Quadratic Formula:4z2+2z-6=0

Short Answer

Step by step solution

Given information

Step 2: Identify the values of a,b,c

Write the quadratic equation formula and substitute the values of a,b,c and then simplify and solve for x

Step 4: check the solutions

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $4 z^{2} + 2 z - 6 = 0$