If α, β are zeroes of the polynomial p(x) = 5x² - 6x + 1, then find the value of α + β + αβ.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 23

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerPolynomials

If $α, β$ are zeroes of the polynomial $p (x) = 5 x^{2} - 6 x + 1$ , then find the value of $α + β + α β$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

You don't need to find the zeroes themselves.

Hint 2

Use the relations: sum of zeroes $= - b / a$ and product $= c / a$ .

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.

Here $a = 5, b = - 6, c = 1$ . Sum of zeroes $α + β = - \frac{b}{a} = \frac{6}{5}$
½ mark
Product of zeroes $α β = \frac{c}{a} = \frac{1}{5}$
½ mark
$α + β + α β = \frac{6}{5} + \frac{1}{5} = \frac{7}{5}$
1 mark

Answer: $\frac{7}{5}$

Where the marks are

$α + β = 6/5$ (½ mark)
$α β = 1/5$ (½ mark)
Adds to get $7/5$ (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 paper2024 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 23

Hints

Step-by-step solution

Revise the chapter

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