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

The zeros of the quadratic polynomial $x^2 + 99x + 127 $ are

  1. Both positive

  2. Both negative

  3. One positive and one negative

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

For x^2 + 99x + 127 = 0, the sum of roots is -99 and the product is 127. Since the product is positive, the roots have the same sign. Since the sum is negative, both roots must be negative.

Multiple choice

The quadratic polynomial whose zeroes are -3, 5 is given by
  1. $\displaystyle x^{2}-3x-15$
  2. $\displaystyle x^{2}-2x-7$
  3. $\displaystyle x^{2}-2x-15$
  4. $\displaystyle x^{2}-2x+15$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If zeroes are a and b, the polynomial is x^2 - (a+b)x + ab. Here a=-3, b=5. Sum = 2, Product = -15. Polynomial = x^2 - 2x - 15.

Multiple choice

Find roots of equation $\displaystyle { a }^{ 4 }{ x }^{ 2 }-{ b }^{ 4 }=0$
  1. $\displaystyle { { b }^{ 2 } }/{ { a }^{ 2 } },-{ { b }^{ 2 } }/{ { a }^{ 2 } }$
  2. $\displaystyle { { b }^{ 2 } }/{ { a }^{ 2 } },{ { b }^{ 2 } }/{ { a }^{ 2 } }$
  3. $\displaystyle { { a }^{ 2 } }/{ { { b }^{ 2 } } },\frac { { a }^{ 2 } }{ { { b }^{ 2 } } } $
  4. $\displaystyle { { a }^{ 2 } }/{ { { b }^{ 2 } } },-\frac { { a }^{ 2 } }{ { { b }^{ 2 } } } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

a^4 * x^2 = b^4 implies x^2 = b^4 / a^4. Taking the square root gives x = +/- b^2 / a^2.