Find the zeroes of the quadratic polynomial x² - 15 and verify the relationship between the zeroes and the coefficients of the polynomial.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 27

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerPolynomials

Find the zeroes of the quadratic polynomial $x^{2} - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Write 15 as $(15)^{2}$ and use $a^{2} - b^{2}$ .

Hint 2

For verification, the coefficient of x is 0. Compare the sum with $- b / a$ and the product with $c / a$ .

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.

Let $p (x) = x^{2} - 15 = x^{2} - (15)^{2} = (x - 15) (x + 15)$ .
1 mark
$p (x) = 0$ when $x = 15$ or $x = - 15$ . So the zeroes are $15$ and $- 15$ .
1 mark
Here $a = 1$ , $b = 0$ , $c = - 15$ . Sum of zeroes $= 15 + (- 15) = 0$ , and $- \frac{b}{a} = - \frac{0}{1} = 0$ . These are equal.
½ mark
Product of zeroes $= 15 \times (- 15) = - 15$ , and $\frac{c}{a} = \frac{- 15}{1} = - 15$ . These are equal. Hence the relationship is verified.
½ mark

Answer: Zeroes are √15 and –√15; sum = 0 = –b/a and product = –15 = c/a (verified)

Where the marks are

Factorises $x^{2} - 15$ as $(x - 15) (x + 15)$ (1 mark)
States the zeroes $\pm 15$ (1 mark)
Verifies sum of zeroes $= - b / a$ (½ mark)
Verifies product of zeroes $= c / a$ (½ 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 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 27

Hints

Step-by-step solution

Revise the chapter

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