Question

If roots of the equation x

2

+ ax + 25 = 0 are in the ratio of 2 : 3 then the value of a is​

Answer 1

Answer:

-25√6/6

Step-by-step explanation:

x^2+ax+25=0

the roots are in the ratio=2:3

the sum of the roots

= -b/a

= -a/1=-a

the product of roots

=c/a

=25/1

=25

let the roots be 2k and 3k say

sum=5k=-a.........(1)

product=

25=2k(3k)

25=6k^2

k^2=25/6

k=5/√6

=5√6/6

so the roots are...

2(5√6/6). 3(5√6/6)

(5√6/3.) ( 5√6/2)

By the EQUATION (1)

5k=-a

a=-5(5√6/6)

=-25√6/6