Chapter 9: Q 9.41 (page 889)

Solve by using the Quadratic Formula: $3 y^{2} - 5 y + 2 = 0$

Short Answer

Expert verified

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

Step by step solution

Given information

We are given an equation $3 y^{2} - 5 y + 2 = 0$

Identify the values of a,b,c

On comparing with standard form we get the values as $a = 3, b = - 5, c = 2$

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

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

Substituting the values of $a, b, c$ we get,

$y = \frac{- (- 5) \pm \sqrt{25 - 4 (3) (2)}}{2 (3)} y = \frac{5 \pm \sqrt{25 - 24}}{6} y = \frac{5 \pm 1}{6}$

on further simplifying

$y = \frac{5 + 1}{6} y = \frac{6}{6} y = 1$ and $y = \frac{5 - 1}{6} y = \frac{4}{6} y = \frac{2}{3}$

Check the solutions

Now we substitute $y = 1$
in the quadratic equation

$3 y^{2} - 5 y + 2 3 {(1)}^{2} - 5 (1) + 2 3 - 5 + 2 = 0$

and now we substitute $x = \frac{2}{3}$ in the equation, We get

$3 y^{2} - 5 y + 2 3 {(\frac{2}{3})}^{2} - 5 (\frac{2}{3}) + 2 \frac{4}{3} - \frac{10}{3} + 2 = 0$

Conclusion

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

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Solve by using the Quadratic Formula: $3 y^{2} - 5 y + 2 = 0$

Short Answer

Step by step solution

Given information

Identify the values of a,b,c

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

Check the solutions

Conclusion

One App. One Place for Learning.

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Solve by using the Quadratic Formula:3y2-5y+2=0

Short Answer

Step by step solution

Given information

Identify the values of a,b,c

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

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

Geometry

Logic and Functions

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $3 y^{2} - 5 y + 2 = 0$