Quantitative Aptitude

Algebra

3,715 Questions
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Algebra Questions

Multiple choice

If $\alpha$ and $\beta$ are roots of the quadratic equation $x^2-2x+3=0$ then quadratic equation whose roots are $\displaystyle \frac{\alpha -1}{\alpha +1}, \frac{\beta -1}{\beta +1}$.
  1. $\displaystyle 3x^{2}+2x+1= 0.$
  2. $\displaystyle 3x^{2}-2x+1= 0.$
  3. $\displaystyle 2x^{2}-3x-1= 0.$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let y = (x-1)/(x+1). Then x = (1+y)/(1-y). Substituting into x^2 - 2x + 3 = 0 gives ((1+y)/(1-y))^2 - 2((1+y)/(1-y)) + 3 = 0. Simplifying leads to 3y^2 - 2y + 1 = 0.

Multiple choice

John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $124$. From the quadratic equation to find how many marbles they had to start with, if John had $x$ marbles.
  1. $36,9$
  2. $20,25$
  3. $30,15$
  4. $27, 18$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let John have x, Jivanti have 45-x. After losing 5, John has x-5, Jivanti has 40-x. (x-5)(40-x) = 124 => 40x - x^2 - 200 + 5x = 124 => x^2 - 45x + 324 = 0. Factors are (x-36)(x-9) = 0. So x = 36 or 9.

Multiple choice

Solve the equation $4 + x^{2} = 2x^{2} - 5$.
  1. $\left \{x : x = 3\right \}$
  2. $\left \{x : x = -3\right \}$
  3. $\left \{x : x = \pm 3\right \}$
  4. $\left \{x : x = -1\right \}$
  5. $\left \{x : x = 1\right \}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

4 + x^2 = 2x^2 - 5. Rearranging gives x^2 = 9. Therefore, x = 3 or x = -3.