Quadratic formula — Class 10 CBSE Mathematics MCQs with Solutions
Free Class 10 CBSE Mathematics Quadratic formula MCQs with step-by-step solutions (2 questions). Part of Quadratic Equations. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Quadratic formula · medium · theory
Why is the quadratic formula $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ more general than factorisation?
A. Because it works for any quadratic, even when roots are irrational or complex, whereas factorisation requires real roots ✓ Correct
B. Because it gives integer roots only
C. Because it simplifies the calculation of coefficients
D. Because it avoids the need to identify $a$, $b$, and $c$
Solution: Factorisation over the reals works only when the quadratic has real (typically rational) roots, so it can be written as $(px+q)(rx+s)=0$. The quadratic formula, however, applies universally—it produces real roots when $\Delta \geq 0$, complex roots when $\Delta < 0$. This makes the formula the universal tool for solving any quadratic.
Q2 — Quadratic formula · hard · theory
Prove conceptually why the quadratic formula $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ must contain a $\pm$ sign, resulting in two values.
A. Because completing the square on $ax^2 + bx + c = 0$ yields $(x + \frac{b}{2a})^2 = \frac{b^2-4ac}{4a^2}$, and taking the square root of both sides gives two solutions: $\pm$ ✓ Correct
B. Because quadratic equations always have two roots by definition
C. Because the coefficients $a$, $b$, $c$ are arbitrary
D. Because the discriminant must be positive
Solution: When we complete the square: $a(x^2 + \frac{b}{a}x) + c = 0$ becomes $a(x + \frac{b}{2a})^2 = \frac{b^2-4ac}{4a}$, so $(x + \frac{b}{2a})^2 = \frac{b^2-4ac}{4a^2}$. Taking the square root: $x + \frac{b}{2a} = \pm\sqrt{\frac{b^2-4ac}{4a^2}}$, giving $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$. The $\pm$ reflects the fundamental fact that a square root has two values (positive and negative).