Question

The equations x2 - 6x + a = 0 and x2 - bx + 6 = 0
have one root in common. The other root of the first and
second equations are integers in the ratio 4:3. Find the
common root.​

Answer 1

Step-by-step explanation:

let m be the common root

the non common roots are 4n and 3n (4:3)

hence the roots of the first equation are

(m, 4n) and the roots of second equation are

(m, 3n)

using the property of sum and product of roots,

m+4n = 6........(1)

m+3n = b.......(2)

m*4n = = a....(3)

m*3n = 6....(4)

(4) gives

mn = 2

(3) and value of mn give

a = 4mn = 4*2 = 8

hence first eqn is

x2 -6x + 8 = 0

on solving we get

x = 2 and 4

since roots are integers hence 2 must be the common root.