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

Equation x2 + 5x – 7 = 0 has roots a and b. Equation 2x2 + px + q = 0 has roots a + 1 and b + 1. Find p + q.
1. 6
2. 0
3. -16
4. 2

Choice C. -16

## Detailed Solution

Given, x2 + 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 2x2 + 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.

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