Find the discriminant of the quadratic equation 3x² - 2x + 1/3 = 0 and hence find the nature of its roots.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 23(A)

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section B, question 23(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(A) · 2 marks · Very short answerQuadratic Equations

Find the discriminant of the quadratic equation $3 x^{2} - 2 x + \frac{1}{3} = 0$ and hence find the nature of its roots.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Discriminant is $b^{2} - 4 a c$ .

Hint 2

If $D = 0$ , what can you say about the roots?

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.

Comparing with $a x^{2} + b x + c = 0$ : $a = 3$ , $b = - 2$ , $c = \frac{1}{3}$
½ mark
$D = b^{2} - 4 a c = (- 2)^{2} - 4 (3) (\frac{1}{3}) = 4 - 4 = 0$
1 mark
Since $D = 0$ , the roots are real and equal.
½ mark

Answer: D = 0; roots are real and equal

Where the marks are

Identifies a, b, c (½ mark)
Computes $D = 0$ (1 mark)
States roots are real and equal (½ 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 paper2023 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 23(A)

Hints

Step-by-step solution

Revise the chapter

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