Start learning →

GRE Quadratic Equations — practice questions

Explore 78 free Quadratic Equations questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Quadratic Equations with Quill →

Quadratic Equations questions and exercises with answers

Showing questions 1–30 of 78.

If the discriminant of a quadratic equation is negative, what can be concluded about its roots?Read the answer and worked solution →For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?Read the answer and worked solution →Find the roots of $2x^2-5x+3=0$ by factorisation.Read the answer and worked solution →What is the maximum number of real roots a quadratic equation can have?Read the answer and worked solution →If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a\neq 0$, then which statement must be true?Read the answer and worked solution →Which equation appears cubic at first glance but actually simplifies to a quadratic equation?Read the answer and worked solution →Which of the following is NOT a quadratic equation after simplification?Read the answer and worked solution →$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →$\sin(A + B) = $Read the answer and worked solution →$\cos 2\theta$ equals:Read the answer and worked solution →If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:Read the answer and worked solution →$\cos 3\theta$ equals:Read the answer and worked solution →sin(0°) equals:Read the answer and worked solution →cos(90°) equals:Read the answer and worked solution →sin²θ + cos²θ equals:Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →In which quadrant is sin θ positive and cos θ negative?Read the answer and worked solution →sec θ is defined as:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →cos(A + B) equals:Read the answer and worked solution →sin(60°) cos(30°) + cos(60°) sin(30°) equals:Read the answer and worked solution →If sin θ = 3/5 (θ in Q1), find cos θ:Read the answer and worked solution →Find cos(75°) using cos(A + B):Read the answer and worked solution →sin(2θ) equals:Read the answer and worked solution →Find sin(15°):Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →For 0 ≤ θ < 2π, solutions of sin θ = 1/2:Read the answer and worked solution →1 - cos²θ equals:Read the answer and worked solution →sin(A) + sin(B) equals (sum-to-product):Read the answer and worked solution →In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:Read the answer and worked solution →

Worked practice questions

If the discriminant of a quadratic equation is negative, what can be concluded about its roots?

  1. The equation has two distinct real roots
  2. The equation has two equal real roots
  3. The equation has no real roots
  4. The equation has exactly one real root
Show answer and solution

Correct answer: C. The equation has no real roots

If $b^2-4ac<0$, then the square root term in the quadratic formula is not a real number. **Therefore, the quadratic equation has no real roots.**

Open this question →

For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?

  1. $b^2+4ac$
  2. $4ac-b^2$
  3. $b^2-4ac$
  4. $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Show answer and solution

Correct answer: C. $b^2-4ac$

The discriminant of the quadratic equation $ax^2+bx+c=0$ is the expression under the square root in the quadratic formula, namely $b^2-4ac$. It determines the nature of the roots.

Open this question →

Find the roots of $2x^2-5x+3=0$ by factorisation.

  1. $x=\frac{3}{2},\ 1$
  2. $x=\frac{5}{2},\ 3$
  3. $x=-\frac{3}{2},\ -1$
  4. $x=\frac{2}{3},\ 1$
Show answer and solution

Correct answer: A. $x=\frac{3}{2},\ 1$

Factorise $2x^2-5x+3$ by splitting the middle term: $2x^2-2x-3x+3=2x(x-1)-3(x-1)=(2x-3)(x-1)$. So $(2x-3)(x-1)=0$, giving $2x-3=0$ or $x-1=0$. **Hence the roots are $x=\frac{3}{2}$ and $x=1$.**

Open this question →

How to practise

  1. Choose a Quadratic Equations question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Quadratic Equations practice for GRE. Read explanations as you go. No signup form needed to start.

Practise Quadratic Equations →

More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits