One root of the equation is and are rational numbers .
Find the value of .
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3 + 8 = 1 + 2 .
As a and b are rational and one root is irrational, the other root must also be irrational and it must also be the conjugate of that root.
Thus the second root is 1 − 2 .
Now we get the required quadratic by multiplying ( x − ( 1 + 2 ) ) ( x − ( 1 − 2 ) ) , but an easier method is by using Vieta's Formula.
By Vieta's Formula, sum of the roots is 1 − a = 1 + 2 + 1 − 2 or a = − 2 .
and product of the roots is 1 b = ( 1 + 2 ) ( 1 − 2 ) = − 1 or b = − 1 .
Thus 1 5 a b = 1 5 × − 2 × − 1 = 3 0 .