[GMAT math practice question]
p and q are the roots of the equation x^2+ax+b=0. What is an expression for p^2q + pq^2 in terms of a and b?
A. ab
B. -ab
C. a^2b
D. ab^2
E. a^2b^2
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p and q are the roots of the equation x^2+ax+b=0. What is an
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Max@Math Revolution
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If p and q are roots of the quadratic equation x^2 + ax + b = 0, then the quadratic equation can be written as (x-p)(x-q) = 0 or x^2 -(p+q)x + pq = 0.
Thus, p + q = -a and pq = b.
So,
p^2q + pq^2 = pq(p+q) = b*(-a) = -ab
Therefore, B is the answer.
Answer: B
If p and q are roots of the quadratic equation x^2 + ax + b = 0, then the quadratic equation can be written as (x-p)(x-q) = 0 or x^2 -(p+q)x + pq = 0.
Thus, p + q = -a and pq = b.
So,
p^2q + pq^2 = pq(p+q) = b*(-a) = -ab
Therefore, B is the answer.
Answer: B
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