Find the value(s) of 'k' so that the quadratic equation 4x² + kx + 1 = 0 has real and equal roots.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 24(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerQuadratic Equations

Find the value(s) of ' $k$ ' so that the quadratic equation $4 x^{2} + k x + 1 = 0$ has real and equal roots.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Which quantity decides the nature of the roots of a quadratic equation?

Hint 2

Put $b^{2} - 4 a c = 0$ with $a = 4$ , $b = k$ , $c = 1$ .

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: $D = b^{2} - 4 a c = 0$ . Here $a = 4$ , $b = k$ , $c = 1$ .
½ mark
$k^{2} - 4 (4) (1) = 0 \Rightarrow k^{2} - 16 = 0$
1 mark
$k^{2} = 16 \Rightarrow k = \pm 4$
½ mark

Answer: $k = 4$ or $k = - 4$

Where the marks are

States the condition $D = 0$ (½ mark)
Forms $k^{2} - 16 = 0$ (1 mark)
Gets $k = \pm 4$ (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

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 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 24(a)

Hints

Step-by-step solution

Revise the chapter

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