Question

Form the equation whose
roots are 10 times those of
x^3+27+5=0​

Answer 1

Answer:

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