Answer the following. (a) Solve the equation 4x² - 9x + 3 = 0, using quadratic formula. (b) Find the nature of roots of the equation 3x² - 4√(3)x + 4 = 0.

x=(9+√(33))/(8) or x=(9-√(33))/(8)

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 21(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerQuadratic Equations

Answer the following.

(a)
Solve the equation $4 x^{2} - 9 x + 3 = 0$ , using quadratic formula.
0 marks
(b)
Find the nature of roots of the equation $3 x^{2} - 43 x + 4 = 0$ .
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Write down the values of a, b and c first.

Hint 2

Work out $b^{2} - 4 a c$ , then substitute into $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$ .

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.

Compare $4 x^{2} - 9 x + 3 = 0$ with $a x^{2} + b x + c = 0$ : $a = 4, b = - 9, c = 3$ .
Discriminant $D = b^{2} - 4 a c = (- 9)^{2} - 4 (4) (3) = 81 - 48 = 33$ .
1 mark
By the quadratic formula, $x = \frac{- b \pm D}{2 a} = \frac{9 \pm 33}{8}$ .
So the roots are $\frac{9 + 33}{8}$ and $\frac{9 - 33}{8}$ .
1 mark

Answer: $x = \frac{9 + 33}{8}$ or $x = \frac{9 - 33}{8}$

Where the marks are

Finds the discriminant $D = 33$ (1 mark)
Applies the quadratic formula to get $x = \frac{9 \pm 33}{8}$ (1 mark)

Revise the chapter

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

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 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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