KEAM 2015 Math Paper

Let the roots of the given equation 2x2+3x+5=0 be α and β
Then, ‌‌α+β=−‌

3

2

and αβ=‌

5

2

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(−‌

3

2

)=−‌

9

2

Also, α′⋅β′=(3α)(3β)=9αβ
=9(‌

5

2

)=‌

45

2

Hence, required equation is
x2−(−‌

9

2

)x+‌

45

2

=0
⇒‌‌2x2+9x+45=0