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Chapter 9: Q 9.41 (page 889)

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

Short Answer

Expert verified

The solution of the above equation isy=1andy=23

Step by step solution

01

Given information

We are given an equation3y2-5y+2=0

02

Identify the values of a,b,c

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

03

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

y=-b卤b2-4ac2a

Substituting the values of a,b,cwe get,

y=-(-5)卤25-4(3)(2)2(3)y=5卤25-246y=5卤16

on further simplifying

y=5+16y=66y=1andy=5-16y=46y=23

04

Check the solutions

Now we substitute y=1
in the quadratic equation

3y2-5y+23(1)2-5(1)+23-5+2=0

and now we substitute x=23in the equation, We get

3y2-5y+23(23)2-5(23)+243-103+2=0

05

Conclusion

The roots of the equation isy=1and y=23

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