A quadratic polynomial having zeroes -√(5/2) and √(5/2) is (A) x²-5√(2)x+1 (B) 8x²-20 (C) 15x²-6 (D) x²-2√(5)x-1

MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 8

From the official CBSE sample question paper for 2024-25, section A, question 8, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q8 · 1 mark · MCQPolynomials

A quadratic polynomial having zeroes $- \frac{5}{2}$ and $\frac{5}{2}$ is

(A) $x^{2} - 52 x + 1$
(B) $8 x^{2} - 20$
(C) $15 x^{2} - 6$
(D) $x^{2} - 25 x - 1$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Find the sum and the product of the two zeroes.

Hint 2

Any non-zero multiple of $x^{2} - (sum) x + product$ has the same zeroes.

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.

Sum of zeroes $= 0$ and product of zeroes $= - \frac{5}{2}$ .
So the polynomial is $k (x^{2} - \frac{5}{2})$ . Taking $k = 8$ gives $8 x^{2} - 20$ . The answer is option (B).
1 mark

Answer: $8 x^{2} - 20$ , option (B)

Where the marks are

Forms $x^{2} - \frac{5}{2}$ from the sum and product of zeroes and matches it with $8 x^{2} - 20$ (1 mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Relationship Between Zeros and Coefficients

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25 (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 sample paper 2024-25: question 8

Hints

Step-by-step solution

Revise the chapter

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