The value of k for which the roots of the quadratic equation 6x² + 4kx + k = 0 are real and equal, is (A) 0 (B) 3/4 (C) (-3)/(2) (D) 2/3

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 2

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQQuadratic Equations

The value of k for which the roots of the quadratic equation $6 x^{2} + 4 k x + k = 0$ are real and equal, is

(A)0
(B) $\frac{3}{4}$
(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 430/5/1.

Hints

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

Hint 1

Real and equal roots means the discriminant is zero.

Hint 2

Solve $16 k^{2} - 24 k = 0$ and compare with the options.

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 equal roots, $D = b^{2} - 4 a c = 0$ : $(4 k)^{2} - 4 (6) (k) = 16 k^{2} - 24 k = 0$ .
$8 k (2 k - 3) = 0 \Rightarrow k = 0$ or $k = \frac{3}{2}$ . Among the options only $0$ appears, so option (A).
1 mark

Answer: k = 0, option (A)

Where the marks are

Uses $D = 0$ to get $k = 0$ or $3/2$ and chooses 0 (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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 2

Hints

Step-by-step solution

Revise the chapter

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