If the three equations x 2 + ax + 12 = 0, x 2 + bx + 15 = 0 and x 2 + (a + b) x + 36 = 0 have a common positive root, find a & b and also the roots of the equation.
Text Solution
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Sol. We have 
Let the common root be m
So, m will satisfy all three equations
Adding (v) and (vi), we get
Subtracting (vi) from (vii) we get
or 
(which is not possible)
Put 
in eqn (iv)
Put 
in eqn (v) we get
Substituting 
in (i) we get
Roots are 3 and 4
Substituting 
in (ii) we get
Roots are 3 and 5
Substituting 
in (iii) we get
Roots are 12 and 3
∴ the possible common root is 
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