Quantitative Aptitude

Algebra

3,715 Questions
All Polynomial Roots and Coefficients 2451 Zero-Product Root Finding 667 Linear System Manipulation 162 Polynomial Theorems and Reduction 85 Algebraic Identity Simplification 82 Surds and Indices 70 Modulus and Absolute Value 54 Algebraic Expression Substitution 46 Algebraic Fraction Simplification 33 Logarithmic Equations 25 Repeated Series Sum 12 Linear Equation Word Problems 9

Algebra Questions

Multiple choice

Roots of quadratic equation $5x^2\,-\,22x\,-\,15\,=\,0$ are
  1. $\displaystyle-\,5, \,\frac{-3}{5}$
  2. $\displaystyle\,5, \,\frac{3}{5}$
  3. $\displaystyle\,5, \,\frac{-3}{5}$

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

5x^2 - 22x - 15 = 0. Using the quadratic formula: x = [22 +/- sqrt(484 - 4(5)(-15))] / 10 = [22 +/- sqrt(484 + 300)] / 10 = [22 +/- sqrt(784)] / 10 = [22 +/- 28] / 10. Roots are 50/10 = 5 and -6/10 = -3/5.

Multiple choice

Find the roots of the following quadratic equation $z^2\,+\,6z\,-\,8\,=\,0$
  1. $z\,=\,-3\,\pm\,\sqrt{19}$
  2. $z\,=\,-3\,\pm\,\sqrt{17}$
  3. $z\,=\,-2\,\pm\,\sqrt{17}$
  4. $z\,=\,-3\,\pm\,\sqrt{15}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the quadratic formula z = (-b +/- sqrt(b^2 - 4ac)) / 2a, we get z = (-6 +/- sqrt(36 - 4(1)(-8))) / 2 = (-6 +/- sqrt(36 + 32)) / 2 = (-6 +/- sqrt(68)) / 2 = (-6 +/- 2*sqrt(17)) / 2 = -3 +/- sqrt(17).

Multiple choice

Find the roots of the following quadratic equation $m^2\,-\,3m\,-\,1\,=\,0$
  1. $\displaystyle\,m\,=\,\frac{3\,\pm\,\sqrt{13}}{2}$
  2. $\displaystyle\,m\,=\,\frac{2\,\pm\,\sqrt{13}}{2}$
  3. $\displaystyle\,m\,=\,\frac{3\,\pm\,\sqrt{11}}{2}$
  4. $\displaystyle\,m\,=\,\frac{3\,\pm\,\sqrt{9}}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the quadratic formula m = [-b +/- sqrt(b^2 - 4ac)] / 2a for m^2 - 3m - 1 = 0: a=1, b=-3, c=-1. m = [3 +/- sqrt((-3)^2 - 4(1)(-1))] / 2 = [3 +/- sqrt(9 + 4)] / 2 = (3 +/- sqrt(13)) / 2.

Multiple choice

Find the roots of the following quadratic equation: $y^2\,=\,3\,+\,4y$
  1. $y\,=\,2\,\pm\,\sqrt2$
  2. $y\,=\,2\,\pm\,\sqrt7$
  3. $y\,=\,2\,\pm\,\sqrt5$
  4. $y\,=\,2\,\pm\,\sqrt6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rearrange the equation to y^2 - 4y - 3 = 0. Using the quadratic formula y = (-b +/- sqrt(b^2 - 4ac)) / 2a, we get y = (4 +/- sqrt(16 - 4(1)(-3))) / 2 = (4 +/- sqrt(28)) / 2 = (4 +/- 2*sqrt(7)) / 2 = 2 +/- sqrt(7).

Multiple choice

Find the roots of following quadratic equation $2x^2\,-\,x\,-\,4\,=\,0$
  1. $\displaystyle\,x\,=\,\frac{2\,\pm\,\sqrt{33}}{4}$
  2. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt{33}}{4}$
  3. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt{33}}{2}$
  4. $\displaystyle\,x\,=\,\frac{1\,\pm\,\sqrt{22}}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a. Here a=2, b=-1, c=-4. x = (1 +/- sqrt((-1)^2 - 4*2*(-4))) / (2*2) = (1 +/- sqrt(1 + 32)) / 4 = (1 +/- sqrt(33)) / 4.

Multiple choice

Find the roots of following quadratic equation $7x\,+\,1\,=\,6x^2$
  1. $\displaystyle\,x\,=\,\frac{5\,\pm\,\sqrt{73}}{12}$
  2. $\displaystyle\,x\,=\,\frac{2\,\pm\,\sqrt{73}}{12}$
  3. $\displaystyle\,x\,=\,\frac{3\,\pm\,\sqrt{73}}{12}$
  4. $\displaystyle\,x\,=\,\frac{7\,\pm\,\sqrt{73}}{12}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rearrange to 6x^2 - 7x - 1 = 0. Using quadratic formula x = [-b +/- sqrt(b^2 - 4ac)] / 2a: x = [7 +/- sqrt(49 - 4(6)(-1))] / 12 = [7 +/- sqrt(49 + 24)] / 12 = [7 +/- sqrt(73)] / 12.