Find the zeroes of the quadratic polynomial x² + 6x + 8 and verify the relationship between the zeroes and the coefficients.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 26

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerPolynomials

Find the zeroes of the quadratic polynomial $x^{2} + 6 x + 8$ and verify the relationship between the zeroes and the coefficients.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Find two numbers with product 8 and sum 6.

Hint 2

Then compare sum and product of zeroes with $- \frac{b}{a}$ and $\frac{c}{a}$ .

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.

$x^{2} + 6 x + 8 = x^{2} + 4 x + 2 x + 8 = (x + 4) (x + 2)$
1 mark
Zeroes: $x = - 4$ and $x = - 2$
1 mark
Sum of zeroes $= - 4 + (- 2) = - 6 = \frac{- 6}{1} = \frac{- coeff. of x}{coeff. of x ^{2}}$
½ mark
Product of zeroes $= (- 4) (- 2) = 8 = \frac{8}{1} = \frac{constant term}{coeff. of x ^{2}}$ . Relationship verified.
½ mark

Answer: Zeroes −4 and −2; sum −6 = −b/a, product 8 = c/a (verified)

Where the marks are

Factorises $(x + 4) (x + 2)$ (1 mark)
Writes zeroes −4, −2 (1 mark)
Verifies sum = −b/a (½ mark)
Verifies product = c/a (½ mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Zeros of a Polynomial

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/4/1 (Basic): 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 Basic 2023: question 26

Hints

Step-by-step solution

Revise the chapter

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