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What is the highest integral value of 'k' for which the quadratic equation x2 - 6x + k = 0 will have two real and distinct roots?
- a)9
- b)7
- c)3
- d)8
- e)12
Correct answer is option 'D'. Can you explain this answer?
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What is the highest integral value of 'k' for which the quadra...
Step 1: Nature of Roots of Quadratic Equation Theory
D is called the Discriminant of a quadratic equation.
D = b2 - 4ac for quadratic equations of the form ax2 + bx + c = 0.
If D > 0, roots of such quadratic equations are Real and Distinct
If D = 0, roots of such quadratic equations are Real and Equal
If D < 0, roots of such quadratic equations are Imaginary. i.e., such quadratic equations will NOT have real roots.
In this GMAT sample question in algebra, we have to determine the largest integer value that ‘k’ can take such that the discriminant of the quadratic equation is positive.
D = b2 - 4ac for quadratic equations of the form ax2 + bx + c = 0.
If D > 0, roots of such quadratic equations are Real and Distinct
If D = 0, roots of such quadratic equations are Real and Equal
If D < 0, roots of such quadratic equations are Imaginary. i.e., such quadratic equations will NOT have real roots.
In this GMAT sample question in algebra, we have to determine the largest integer value that ‘k’ can take such that the discriminant of the quadratic equation is positive.
Step 2: Compute maximum value of k that will make the discriminant of the quadratic equation positive
The given quadratic equation is x2 - 6x + k = 0.
In this equation, a = 1, b = -6 and c = k
The value of the discriminant, D = 62 - 4 * 1 * k
We have compute values of 'k' for which D > 0.
i.e., 36 – 4k > 0
Or 36 > 4k or k < 9.
In this equation, a = 1, b = -6 and c = k
The value of the discriminant, D = 62 - 4 * 1 * k
We have compute values of 'k' for which D > 0.
i.e., 36 – 4k > 0
Or 36 > 4k or k < 9.
The question is "What is the highest integer value that k can take?"
If k < 9, the highest integer value that k can take is 8.
If k < 9, the highest integer value that k can take is 8.
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What is the highest integral value of 'k' for which the quadra...
Step 1: Nature of Roots of Quadratic Equation Theory
D is called the Discriminant of a quadratic equation.
D = b2 - 4ac for quadratic equations of the form ax2 + bx + c = 0.
If D > 0, roots of such quadratic equations are Real and Distinct
If D = 0, roots of such quadratic equations are Real and Equal
If D < 0, roots of such quadratic equations are Imaginary. i.e., such quadratic equations will NOT have real roots.
In this GMAT sample question in algebra, we have to determine the largest integer value that ‘k’ can take such that the discriminant of the quadratic equation is positive.
D = b2 - 4ac for quadratic equations of the form ax2 + bx + c = 0.
If D > 0, roots of such quadratic equations are Real and Distinct
If D = 0, roots of such quadratic equations are Real and Equal
If D < 0, roots of such quadratic equations are Imaginary. i.e., such quadratic equations will NOT have real roots.
In this GMAT sample question in algebra, we have to determine the largest integer value that ‘k’ can take such that the discriminant of the quadratic equation is positive.
Step 2: Compute maximum value of k that will make the discriminant of the quadratic equation positive
The given quadratic equation is x2 - 6x + k = 0.
In this equation, a = 1, b = -6 and c = k
The value of the discriminant, D = 62 - 4 * 1 * k
We have compute values of 'k' for which D > 0.
i.e., 36 – 4k > 0
Or 36 > 4k or k < 9.
In this equation, a = 1, b = -6 and c = k
The value of the discriminant, D = 62 - 4 * 1 * k
We have compute values of 'k' for which D > 0.
i.e., 36 – 4k > 0
Or 36 > 4k or k < 9.
The question is "What is the highest integer value that k can take?"
If k < 9, the highest integer value that k can take is 8.
If k < 9, the highest integer value that k can take is 8.
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What is the highest integral value of 'k' for which the quadratic equation x2- 6x + k = 0 will have two real and distinct roots?a)9b)7c)3d)8e)12Correct answer is option 'D'. Can you explain this answer?
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