Linear and Quadratic Equations

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

Roots - Quadratic Equation

    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

 

  • Correct Answer
    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 = = -5.

Product of the roots = ab = = -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 = = -5 +2 = -3 = => -p = -6 => p =6.

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

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

Correct Answer: -16



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Solving equations well is an integral part to cracking any competitive exam. Get cartloads of practice on these two topics.