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

Form the quadratic equation if its roots are: $-3$ and $-11$
  1. $x^2\,-\,14x\,+\,33\,=\,0$
  2. $x^2\,+\,14x\,+\,33\,=\,0$
  3. $x^2\,+\,14x\,-\,33\,=\,0$
  4. $x^2\,+\,14x\,+\,18\,=\,0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A quadratic equation with roots r1 and r2 is x^2 - (r1+r2)x + (r1*r2) = 0. Here, r1+r2 = -3 + -11 = -14 and r1*r2 = 33. The equation is x^2 - (-14)x + 33 = 0, which is x^2 + 14x + 33 = 0.

Multiple choice

Form the quadratic equation if its roots are: $5$ and $-7$
  1. $x^2\,+\,2x\,-\,35\,=\,0$
  2. $x^2\,+\,x\,-\,35\,=\,0$
  3. $x^2\,+\,3x\,-\,35\,=\,0$
  4. $x^2\,+\,4x\,-\,35\,=\,0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A quadratic equation with roots r1 and r2 is given by x^2 - (r1 + r2)x + (r1 * r2) = 0. Here, roots are 5 and -7, so the sum is -2 and the product is -35. The equation is x^2 - (-2)x + (-35) = 0, which is x^2 + 2x - 35 = 0.

Multiple choice

Form the quadratic equation if its roots are: $\displaystyle\,-2$ and $\cfrac{11}{2}$
  1. $2x^2\,+\,7x\,-\,22\,=\,0$
  2. $2x^2\,-\,7x\,-\,9\,=\,0$
  3. $2x^2\,-\,7x\,-\,22\,=\,0$
  4. $2x^2\,-\,7x\,-\,11\,=\,0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If roots are r1 and r2, the equation is x^2 - (r1+r2)x + (r1*r2) = 0. Here, r1 = -2 and r2 = 11/2. Sum = -2 + 5.5 = 3.5 = 7/2. Product = -2 * 11/2 = -11. Equation: x^2 - (7/2)x - 11 = 0, which multiplies to 2x^2 - 7x - 22 = 0.

Multiple choice

Solve the following equations. $x^4\,-\,3x^2\,+\,2\,=\,0$, roots are
  1. $x\,=\,\pm\,\sqrt3,\,\pm\,1$
  2. $x\,=\,\pm\,\sqrt2,\,\pm\,1$
  3. $x\,=\,\pm\,\sqrt2,\,\pm\,3$

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let y = x^2. The equation becomes y^2 - 3y + 2 = 0, which factors to (y - 1)(y - 2) = 0. So y = 1 or y = 2. Since y = x^2, x^2 = 1 (x = +/- 1) or x^2 = 2 (x = +/- sqrt(2)).

Multiple choice

Form the quadratic equation with rational coefficients, if its one of the root is $2\,+\,\sqrt5$, then the equation is
  1. $2x^2\,-\,4x\,-\,1\,=\,0$
  2. $x^2\,-\,2x\,-\,1\,=\,0$
  3. $x^2\,-\,4x\,-\,1\,=\,0$
  4. $x^2\,-\,4x\,-\,2\,=\,0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Turpentine absorbs ozone (O3). A reduction of 20 ml in 100 ml means 20 ml of O3 was present. The reaction 2O3 -> 3O2 shows that 2 volumes of O3 produce 3 volumes of O2, an increase of 1 volume. Since 20 ml of O3 is present, the increase in volume upon heating is 10 ml.

Multiple choice

Form the quadratic equation if its roots are: $0\,\,and\,\,-4$
  1. $x^2\,+\,x\,=\,0$
  2. $x^2\,+\,4x\,=\,0$
  3. $x^2\,+\,2x\,=\,0$
  4. $x^2\,+\,6x\,=\,0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If roots are r1 and r2, the equation is x^2 - (r1+r2)x + r1*r2 = 0. Here r1=0, r2=-4. Sum = -4, Product = 0. Equation: x^2 - (-4)x + 0 = 0, which is x^2 + 4x = 0.