MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 31

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerQuadratic Equations

Find the value of 'p' for which the quadratic equation $p x (x - 2) + 6 = 0$ has two equal real roots.

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

First expand the equation into the form $a x^{2} + b x + c = 0$ .

Hint 2

Equal roots means $b^{2} - 4 a c = 0$ . Solve for p, and check whether each value keeps the equation quadratic.

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.

Expand: $p x (x - 2) + 6 = 0$ becomes $p x^{2} - 2 p x + 6 = 0$ .
So $a = p$ , $b = - 2 p$ , $c = 6$ .
½ mark
For two equal real roots, the discriminant must be zero: $D = b^{2} - 4 a c = 0$ .
½ mark
$(- 2 p)^{2} - 4 (p) (6) = 0$
$4 p^{2} - 24 p = 0$
1 mark
$4 p (p - 6) = 0$ , so $p = 0$ or $p = 6$ .
½ mark
If $p = 0$ , the equation becomes $6 = 0$ , which is not a quadratic. So $p = 0$ is rejected.
Hence $p = 6$ .
½ mark

Answer: $p = 6$

Where the marks are

Writes the equation in standard form $p x^{2} - 2 p x + 6 = 0$ (½ mark)
Uses the condition $D = 0$ for equal roots (½ mark)
Forms $4 p^{2} - 24 p = 0$ (1 mark)
Factorises to get $p = 0$ or $p = 6$ (½ mark)
Rejects $p = 0$ and gives $p = 6$ (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.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2023: question 31

Hints

Step-by-step solution

Revise the chapter

More questions from Quadratic Equations