Find the discriminant of the quadratic equation 4x² - 5 = 0 and hence comment on the nature of roots of the equation.

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 23(B)

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section B, question 23(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Find the discriminant of the quadratic equation $4 x^{2} - 5 = 0$ and hence comment on the nature of roots of the equation.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

The equation has no $x$ term, so $b = 0$ .

Hint 2

Compute $b^{2} - 4 a c$ and check its sign.

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 $4 x^{2} + 0 \cdot x - 5 = 0$ with $a x^{2} + b x + c = 0$ : $a = 4$ , $b = 0$ , $c = - 5$ .
Discriminant $D = b^{2} - 4 a c = 0^{2} - 4 (4) (- 5) = 80$ .
1½ marks
Since $D = 80 > 0$ , the equation has two distinct real roots (they are $x = \pm \frac{5}{2}$ ).
½ mark

Answer: D = 80 > 0; roots are real and distinct

Where the marks are

Identifies $a, b, c$ and computes $D = b^{2} - 4 a c = 80$ (1½ marks)
Concludes that the roots are real and distinct since $D > 0$ (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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 23(B)

Hints

Step-by-step solution

Revise the chapter

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