Linear Quadratic Answers

Quadratic Equation : CAT 2007 Quant/Math Questions Answers

Question 4 the day : February 12, 2003
The question for the day is from the topic Quadratic Equations in Algebra.

Question
For what values of 'm' is y = 0, if y = x² + (2m + 1)x + m² - 1?   x is a real number.

(1) m >=  -2
(2) m < 0
(3) m = 0
(4) m >=  -1.25

Correct Answer is m >= -1.25 . Correct Choice is (4)
 

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Explanatory Answer

When x is real, then the discriminant of a quadratic equation (ax² + bx + c = 0) >= 0.
i.e. D = b² - 4ac >=  0

In this case, (2m + 1)² >= 4(m² - 1)
4m² + 4m + 1 >= 4(m² - 1)
Solving for m, we get m >= - 1.25