Class 10 Quadratic Equations Mock Test (ICSE)

Topics in Quadratic Equations

• Standard form of a quadratic equation
• Solving by factorisation
• Solving by the quadratic formula
• Nature of roots by the discriminant

Quadratic Equations practice questions with answers

1. Q1Multiple choice·1 mark
   Which of the following equations is a quadratic equation?

   1. (a)$x(x + 1) + 8 = (x + 2)(x - 2)$
   2. (b)$x^2 + 3x = (x - 2)^2$
   3. (c)$x(2x + 3) = x^2 + 2$
   4. (d)$(x + 2)^3 = x^3 + 6x^2 - 4$
   Show answer and step marks

   1. Correct option: (c) $x(2x + 3) = x^2 + 2$. Expanding gives $2x^2 + 3x = x^2 + 2 \implies x^2 + 3x - 2 = 0$, of degree $2$; options (a), (b) and (d) reduce to the linear equations $x + 12 = 0$, $7x - 4 = 0$ and $12x + 12 = 0$.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   If the quadratic equation $3x^2 - 5x + m = 0$ has real and equal roots, then the value of $m$ is:

   1. (a)$-\frac{12}{25}$
   2. (b)$\frac{25}{12}$
   3. (c)$-\frac{25}{12}$
   4. (d)$\frac{12}{25}$
   Show answer and step marks

   1. Correct option: (b) $\frac{25}{12}$. For real and equal roots, discriminant $\Delta = b^2 - 4ac = 0$. Here, $(-5)^2 - 4(3)(m) = 0 \implies 25 - 12m = 0 \implies m = \frac{25}{12}$.+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   The roots of the quadratic equation $x^2 - 7x + 12 = 0$ are:

   1. (a)$2, 6$
   2. (b)$-2, -6$
   3. (c)$-3, -4$
   4. (d)$3, 4$
   Show answer and step marks

   1. Correct option: (d) $3, 4$. Factorising the quadratic expression: $(x - 3)(x - 4) = 0$, giving roots $x = 3$ and $x = 4$.+1

   Answer: (d)
4. Q4Multiple choice·1 mark
   The roots of the quadratic equation $3x^2 - 5x - 2 = 0$ are:

   1. (a)$x = 2, -\frac{1}{3}$
   2. (b)$x = 1, -\frac{2}{3}$
   3. (c)$x = -2, \frac{1}{3}$
   4. (d)$x = -1, \frac{2}{3}$
   Show answer and step marks

   1. Correct option: (a) $x = 2, -\frac{1}{3}$. Applying the quadratic formula $x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-2)}}{2(3)} = \frac{5 \pm \sqrt{25 + 24}}{6} = \frac{5 \pm 7}{6}$, giving $x = 2$ or $x = -\frac{1}{3}$.+1

   Answer: (a)

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