Free GMAT Quadratic Equation Practice Problems
with Solutions – Sample 3

Test your GMAT problem-solving skills with the following set of 10 quadratic equation problems. Detailed solutions are available here.

Question 1

Solve the equation: \[ x^2 + 5x + 6 = 0 \]

Find the values of constants \(k\) and \(m\) such that the equation \[ 2x^2 + kx - m = 0 \] has solutions \(x = 1\) and \(x = -2\).

\(k = 1, m = -2\)
\(k = -2, m = -4\)
\(k = 2, m = 0\)
\(k = 2, m = 4\)
\(k = 0, m = 4

Solve the equation: \[ (x - 1)(x + 3) = 1 - x \]

\(x = 1\) and \(x = -3\)
\(x = 1\) and \(x = -4\)
\(x = 1\) and \(x = 4\)
\(x = 1\) and \(x = 0\)
\(x = 1\) and \(x = 3\)

Solve: \[ 2 - (x - 2)^2 = -18 \]

\(x = 2 + 2\sqrt{5}, x = 2 - 2\sqrt{5}\)
\(x = 2\sqrt{5}, x = -2\sqrt{5}\)
\(x = 20, x = -20\)
\(x = \sqrt{5}, x = -\sqrt{5}\)
\(x = -2 + 2\sqrt{5}, x = -2 - 2\sqrt{5}\)

Find the positive value of \(k\) such that the equation: \[ x^2 + kx + 4 = 0 \] has exactly one solution.

If \(x = 2\) is a solution of \[ (m+2)x^2 = 16 \] find the second solution.

If \(x = -2\) is a solution of \[ \frac{1}{2} a x^2 + 3x - 4 = 0 \] find the second solution.

Find \(b\) and \(c\) so that \[ x^2 + bx + c = 0 \] has solutions \(x = 2\) and \(x = -1\).

\(b = 2, c = -1\)
\(b = -2, c = 1\)
\(b = 2, c = 2\)
\(b = 1, c = 0\)
\(b = -1, c = -2\)

Given \(X + Y = \frac{11}{5}\) and \(XY = \frac{2}{5}\), with \(X > 1\), find \(X\) and \(Y\).

\(X = \frac{1}{5}, Y = 2\)
\(X = 2, Y = \frac{1}{5}\)
\(X = 2, Y = \frac{2}{5}\)
\(X = \frac{3}{5}, Y = \frac{1}{5}\)
\(X = 10, Y = \frac{1}{5}\)

Find \(x > 1\) such that \[ x + \frac{1}{x} = \frac{10}{3} \]