The question is about Sum and product of the roots of a Quadratic Equation. Some details about the product and sum of the roots are given and we need to find out the product of the roots. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 11: 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?

- 6 or 3
- 12 or 2
- 8 or 4
- 12 or 4

12 or 2

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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.

The question is **"If one root is 1 more than the other root, find the product of the roots?"**

Choice B is the correct answer.

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