The question is about Roots of Equation. How you would relate sum and product of roots of two quadratic equations. Framing and solving equations forms the basis of quants. 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 10: Equation x^{2} + 5x – 7 = 0 has roots a and b. Equation 2x^{2} + px + q = 0 has roots a + 1 and b + 1. Find p + q?

- 6
- 0
- -16
- 2

-16

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Given, x^{2} + 5x – 7 = 0 has roots a and b. We know that,

Sum of roots in a quadratic equation = a+b = \\frac{(-5)}{1}\\) = -5.

Product of the roots = ab = \\frac{(-7)}{1}\\) = -7.

Now, The second equation 2x^{2} + px + q = 0 has roots a + 1 and b + 1.

Sum of the roots = a+1+b+1 = a+b+2 = \\frac{(-p)}{2}\\) = -5 +2 = -3 = \\frac{(-p)}{2}\\) => -p = -6 => p =6.

Product of the roots = (a+1)(b+1) = ab+a+b+1 = \\frac{q}{2}\\). We know the values of ab and a+b. Substituting this, we get, -7+(-5)+1 = \\frac{q}{2}\\) => -11 = \\frac{q}{2}\\)=> q =-22.

Hence, p = 6 and q = -22. => p+q = 6 +(-22) = -16.

The question is **"Equation x ^{2} + 5x – 7 = 0 has roots a and b. Equation 2x^{2} + px + q = 0 has roots a + 1 and b + 1. Find p + q?"**

Choice C is the correct answer.

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