The Math Practice Question is from the topic Quadratic Equation in Algebra.
What is the highest integral value of 'k' for which the quadratic equation x2
- 6x + k = 0 have two real and distinct roots?
The correct choice is (D) and the correct answer is 8
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
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.