If equations `x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0,` have a common positive root, then find the values of `aa n dbdot`

Explanation

We have ,
`x^(2) + ax + 12 = 0` (1)
`x^(2) + bx + 15 = 0` (2)
`x^(2) + (a + b) x + 36 = 0` (3)
Adding (1) and (2), we get
`2x^(2)+ (a+ b) x + 27 = 0`
Now subtracting it from the third equation, we get
`x^(2) - 9 = 0 rArr x = 3, 3`
Thus , the common positive root is 3, Hence,
`9 + 12 + 3a = 0`
`rArr a = - 7 and 9 + 3b + 15 = 0 `
`rArr b = -8` .