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You are here: Home » GMAT Problem Solving » Quadratic Equation » Question 1

The Math Practice Question is from the topic Quadratic Equation in Algebra.

Question 1

What is the highest integral value of 'k' for which the quadratic equation x² - 6x + k = 0 have two real and distinct roots?

1. 9
2. 7
3. 3
4. 8
5. 12
   
   

The correct choice is (D) and the correct answer is 8.

Explanatory Answer

Any quadratic equation will have real and distinct roots if the discriminant D > 0

The discriminant 'D' of a quadratic equation ax² + bx + c = 0 is given by b² - 4ac

In this question, the value of D = 6² - 4 * 1 * k

If D > 0, then 36 > 4k or k < 9.

Therefore, the highest integral value that k can take is 8.