Find the nature of roots of the quadratic equation x² + 4x - 3√(2) = 0.

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 24

From the official CBSE sample question paper for 2025-26, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerQuadratic Equations

Find the nature of roots of the quadratic equation $x^{2} + 4 x - 32 = 0$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

The nature of roots depends on the discriminant $b^{2} - 4 a c$ .

Hint 2

Be careful with the sign: $c$ is negative, so $- 4 a c$ becomes positive.

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.

Here $a = 1, b = 4, c = - 32$ . Discriminant $D = b^{2} - 4 a c = 16 - 4 (1) (- 32) = 16 + 122$
1 mark
Since $D = 16 + 122 > 0$ , the equation has two distinct real roots.
1 mark

Answer: $D = 16 + 122 > 0$ ; roots are real and distinct.

Where the marks are

Correct discriminant $16 + 122$ (1 mark)
Concludes roots are real and distinct since $D > 0$ (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 paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 24

Hints

Step-by-step solution

Revise the chapter

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