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Knowledge about the product and sum of the roots is important to solve this one!!

## Sum and product of the roots

Sum of the roots of a quadratic equation is 5 less than the product of the roots. If one root is 1 more than the other root, find the product of the roots?
1. 6 or 3
2. 12 or 2
3. 8 or 4
4. 12 or 4

Choice B. 12 or 2

## Detailed Solution

Sum of the roots = (product of the roots) – 5
Let $r_{1}$ and $r_{2}$ be the two roots
$r_{1} = r_{2} + 1$

Therefore,
$r_{1} + 1 + r_{2} = (r_{1}r_{2}) * r_{2} - 5$
$r_{2} + 1 + r_{2} = (r_{2} + 1) * r_{2} - 5$
$2r_{2} + 6 = (r_{2})^{2} + r_{2}$
$(r_{2})^{2} - r_{2} - 6 = 0$
Solving, we get $r_{2}$ = 3 or -2
Therefore, $r_{2}$ = 4 or -1

Hence product of the two roots is either 12 or 2.

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