Question

The equation whose roots are multiplied by 3 of those of 2x2+3x−1=0 is

Answer 1

Answer:5x  

2

+9x+45=0

Step-by-step explanation:

Let the roots of the given equation 2x  

2

+3x+5=0 be α and β.

Then, α+β=−  

2

3

​

 and αβ=  

2

5

​

 

Let the roots of required equation be α  

′

 

 and β  

′

 

.

It is given that,

α  

′

 

=3α and β  

′

 

=3β

Now, α  

′

 

+β  

′

 

=3α+3β

=3(α+β)

=3(−  

2

3

​

)=−  

2

9

​

 

Also, α  

′

 

⋅β  

′

 

=(3α)(3β)=9αβ

=9(  

2

5

​

)=  

2

45

​

 

Hence, required equation is

x  

2

−(−  

2

9

​

)x+  

2

45

​

=0

⇒2x  

2

+9x+45=0