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Quadratic Equation - January 29, 2004
The GMAT Sample Math question for the day is from the topic Quadratic Equation.
Question
For what value of ‘m’ will the quadratic equation x2 – mx + 4 = 0 have real and equal roots?
A. 16
B. 8
C. 2
D. -4
E. Choice (B) and (C)
The correct choice is (D) and the correct answer is -4.
Explanatory Answer
Any quadratic equation of the form ax2 + bx + c = 0 will have real and equal roots if its discriminant b2 – 4ac = 0.
In the given equation x2 – mx + 4 = 0, a = 1, b = -m and c = 4.
Therefore, b2 – 4ac = m2 – 4(4)(1) = m2 – 16.
As we know, the roots of the given equation are real and equal.
Therefore, m2 – 16 = 0 or m2 = 16 or m = +4 or m = -4.
Hence, answer choice (D) is correct.
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