If the sum of zeroes of the polynomial p(x)=2x²-k√(2) x+1 is √(2), then value of k is: (A) √(2) (B) 2 (C) 2√(2) (D) 1/2

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 1

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQPolynomials

If the sum of zeroes of the polynomial $p (x) = 2 x^{2} - k 2 x + 1$ is $2$ , then value of $k$ is:

(A) $2$
(B)2
(C) $22$
(D) $\frac{1}{2}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Recall the relation between the zeroes and the coefficients of a quadratic.

Hint 2

Sum of zeroes $= - \frac{b}{a}$ . Here $b = - k 2$ and $a = 2$ .

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.

For $a x^{2} + b x + c$ , the sum of zeroes is $- \frac{b}{a}$ . Here $a = 2$ and $b = - k 2$ , so the sum of zeroes is $\frac{k 2}{2}$ .
Given that the sum is $2$ : $\frac{k 2}{2} = 2 \Rightarrow k = 2$ . So the answer is option (B).
1 mark

Answer: k = 2, option (B)

Where the marks are

Uses sum of zeroes $= - b / a$ and gets $k = 2$ , option (B) (1 mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 1

Hints

Step-by-step solution

Revise the chapter

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