Quantitative Aptitude

Algebra

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Algebra Questions

Multiple choice

The equation x2−12x+k= 0 has equal roots. Find k.

  1. 24

  2. 36

  3. 48

  4. 72
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For the equation x^2 - 12x + k = 0 to have equal roots, the discriminant b^2 - 4ac must be 0. Here, b = -12, a = 1, c = k. So, (-12)^2 - 4(1)(k) = 0, which means 144 - 4k = 0, so k = 36.

Multiple choice

The question is based on the following pattern. The problems below contain a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question. Find integers q, if the equation y2 - 2y + q = 0 has rational roots. (A) Only one of the roots is a natural number. (B) The product of the roots is zero.

  1. if the question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.

  2. if the question can be answered by using either statement alone.

  3. if the question can be answered by using both the statement together, but cannot be answered by using either statement alone.

  4. if both the statements taken together are not sufficient and more information is required to solve the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

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Directions: Solve the following quadratic equations and mark the answer as per these codes: I. 7x2 + 10x - 8 = 0 II. 7y2 - 27y + 18 = 0

  1. x > y

  2. x < y

  3. x ≤ y

  4. x ≥ y

  5. x = y, or no relation can be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 7x^2 + 10x - 8 = 0 gives roots x = 0.8 and x = -2. Solving 7y^2 - 27y + 18 = 0 gives roots y = 3 and y = 0.857. Comparing the roots, x is consistently less than y.