The value of 'a' for which ax² + 3x + 1 = 0 has real and equal roots is : (A) 4/9 (B) 9/4 (C) 3/2 (D) 2/3

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 4

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQQuadratic Equations

The value of 'a' for which $a x^{2} + 3 x + 1 = 0$ has real and equal roots is :

(A) $\frac{4}{9}$
(B) $\frac{9}{4}$
(C) $\frac{3}{2}$
(D) $\frac{2}{3}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

What condition on the discriminant gives equal roots?

Hint 2

Set $b^{2} - 4 a c = 0$ and solve for a.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

For real and equal roots, the discriminant must be zero: $D = b^{2} - 4 a c = 0$ .
$3^{2} - 4 (a) (1) = 0 \Rightarrow 9 = 4 a \Rightarrow a = \frac{9}{4}$ , which is option (B).
1 mark

Answer: a = 9/4, option (B)

Where the marks are

Sets $9 - 4 a = 0$ to get $a = \frac{9}{4}$ (1 mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Nature of Roots and Discriminant

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 4

Hints

Step-by-step solution

Revise the chapter

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