GMAT Maths | Quadratic Algebra #9

This GMAT Sample Maths question is from Quadratic Equations. Concept tested: Nature of roots of quadratic equations. Specifically, condition that roots of quadratic equations are real and equal. What values should the discriminant take for the roots to be real and equal? A 600 level GMAT practice question in algebra - quadratic equations discriminant.

Question 9: For what value of 'm' will the quadratic equation x² - mx + 4 = 0 have real and equal roots?

1. 16
2. 8
3. 2
4. -4
5. Choice (B) and (C)

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Video Explanation

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Explanatory Answer

Step 1 of solving this GMAT Quadratic Equations Question: Nature of Roots of Quadratic Equations Theory

D is the Discriminant in a quadratic equation.
D = b² - 4ac for quadratic equations of the form ax² + bx + c = 0.
If D > 0, roots are Real and Unique (Distinct and real roots).
If D = 0, roots are Real and Equal.
If D < 0, roots are Imaginary. The roots of such quadratic equations are NOT real.
The quadratic equation given in this question has real and equal roots. Therefore, its discriminant D = 0.

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Step 2 of solving this GMAT Quadratic Equations Question: Compute discriminant for the equation in terms of ‘m’ and find the value of ‘m’.

In the given equation x² - mx + 4 = 0, a = 1, b = -m and c = 4.
Therefore, the discriminant b² - 4ac = m² - 4(4)(1) = m² - 16.
The roots of the given equation are real and equal.
Therefore, m² - 16 = 0 or m² = 16 or m = +4 or m = -4.

Choice (D) is the answer to this quadratic equations question.