This is aptitude questions and answers section on Quadratic Equations with explanation for various interview, competitive examinations and entrance tests.

1. Find the roots of the quadratic equation: x^{2} + 2x - 15 = 0?
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Answer: Option A

Explanation:

x^{2} + 5x - 3x - 15 = 0

x(x + 5) - 3(x + 5) = 0

(x - 3)(x + 5) = 0

=> x = 3 or x = -5.

2. Find the roots of the quadratic equation: 2x^{2} + 3x - 9 = 0?
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Answer: Option B

Explanation:

2x^{2} + 6x - 3x - 9 = 0

2x(x + 3) - 3(x + 3) = 0

(x + 3)(2x - 3) = 0

=> x = -3 or x = 3/2.

3. The roots of the equation 3x^{2} - 12x + 10 = 0 are?
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Answer: Option D

Explanation:

The discriminant of the quadratic equation is (-12)^{2} - 4(3)(10) i.e., 24. As this is positive but not a perfect square, the roots are irrational and unequal.

4. If the roots of a quadratic equation are 20 and -7, then find the equation?
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Answer: Option C

Explanation:

Any quadratic equation is of the form

x^{2} - (sum of the roots)x + (product of the roots) = 0 ---- (1)

where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x^{2} - 13x - 140 = 0.

5. The sum and the product of the roots of the quadratic equation x^{2} + 20x + 3 = 0 are?
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Answer: Option E

Explanation:

Sum of the roots and the product of the roots are -20 and 3 respectively.