Que : When the equation \(x^2+ax+b=0\) has roots p and q, what is the value of p + q?

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Que : When the equation \(x^2+ax+b=0\) has roots p and q, what is the value of p + q?

(1) a = 4
(2) b = 9

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Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of p + q.

=> Given: \(x^2+ax+b=0\) has ‘p’ and ‘q’ as its roots.

=> (x – p) (x – q)=0 => \(x^2-\left(p+q\right)x+pq=0\)

=> a=-(p+q) and b=pq

=> We have to find the value of a

Condition (1) tells us that a = 4.

=> a = 4 = -(p + q)

=> -( p + q) = 4

=> p + q = -4

The answer is unique, so condition (1) alone is sufficient, according to CMT 2 - there must be only one answer

Condition (2) tells us that it b = 9.

=> b = pq = 9

=> If p = q = 3, then pq = 3 * 3 = 9 => p + q = 3 + 3 = 6

=> But if p =1; q = 9, then pq = 1 * 9 = 9 => p + q = 1 + 9 = 10

The answer is not unique, so condition (1) alone is not sufficient, according to CMT 2 - there must be only one answer.

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Answer: A