Chapter 9: Q. 9.43 (page 890)

Solve by using the Quadratic Formula: $a^{2} - 2 a = 15$

Short Answer

Expert verified

The solution of the equation is $a = 5$ and $a = - 3$

Step by step solution

Given equation

We are given a quadratic equation $a^{2} - 2 a = 15$

Write the equation in standard form by adding -15 to each side. and identify the values of a,b,c

We get,

$a^{2} - 2 a - 15 = 0$

Write quadratic formula and substitute the values of a,b,c

The quadratic formula can be given as

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

on comparing with standard equation we get $x = 1, y = - 2, z = - 15$

On substituting we get

$a = \frac{2 \pm \sqrt{4 - 4 (1) (- 15)}}{2}$

Simplify and find the values of a

On simplifying we get,

$a = \frac{- 2 \pm \sqrt{4 + 60}}{2} a = \frac{- 2 \pm \sqrt{64}}{2} a = \frac{- 2 \pm 8}{2}$

On further simplifying

$a = \frac{- 2 + 8}{2} a = \frac{6}{2} a = 3$ and $a = \frac{- 2 - 8}{2} a = \frac{- 10}{2} a = - 5$

Check the solution

We substitute $x = 5$ in the quadratic equation

$a^{2} - 2 a - 15 {(5)}^{2} - 2 (5) - 15 25 - 10 - 15 = 0$

And now we substitute $x = - 3$ in the above equation

$a^{2} - 2 a - 15 {(- 3)}^{2} - 2 (- 3) - 15 9 + 6 - 15 = 0$

Conclusion

The roots of the above equation is $a = 5$ and $a = - 3$

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Solve by using the Quadratic Formula: $a^{2} - 2 a = 15$

Short Answer

Step by step solution

Given equation

Write the equation in standard form by adding -15 to each side. and identify the values of a,b,c

Write quadratic formula and substitute the values of a,b,c

Simplify and find the values of a

Check the solution

Conclusion

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Solve by using the Quadratic Formula:a2-2a=15

Short Answer

Step by step solution

Given equation

Write the equation in standard form by adding -15 to each side. and identify the values of a,b,c

Write quadratic formula and substitute the values of a,b,c

Simplify and find the values of a

Check the solution

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $a^{2} - 2 a = 15$