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Question 14 of 34 · Quadratic Equations
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NIMCET 2023

If the equation has four real solutions, then find the value of .

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Answer: Option C —

Detailed Solution

1

: roots and , vertex .

2

Taking the modulus reflects the part between and upwards, giving a hump of height at .

3

A horizontal line cuts this W-shaped graph in 4 points only when it lies strictly between the x-axis and the top of the hump: .

figure

✓ Check

Take : and have discriminants and , giving 4 distinct roots.

⚠ Common trap

(B) touches the top of the hump at , so the roots are and : only 3 solutions.

Quick tip

; the reflected hump has height 1, so 4 roots need

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Quadratic Equations — Preparation

This question tests your understanding of Quadratic Equations, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

A quadratic equation has the form ax^2 + bx + c = 0, where a is not zero. This topic covers solving quadratics by factorisation and by the quadratic formula, the nature of roots using the discriminant b^2 - 4ac, the sum (-b/a) and product (c/a) of roots, and forming an equation from its roots. In aptitude exams, a common question type gives two quadratic equations and asks you to compare their roots (whether x > y, x < y and so on). In engineering and MCA entrance exams, questions also test conditions on roots, common roots, and symmetric expressions such as the sum of squares of roots. Using the sum and product of roots is usually far faster than finding the roots themselves. Practise the quadratic equation questions below, each with a step-by-step solution.

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