If 'α' and 'β' are the zeroes of the polynomial p(y) = y² - 5y + 3, then find the value of α^4β³ + α³β^4.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 24(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerPolynomials

If ' $α$ ' and ' $β$ ' are the zeroes of the polynomial $p (y) = y^{2} - 5 y + 3$ , then find the value of $α^{4} β^{3} + α^{3} β^{4}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Find the sum and the product of the zeroes from the coefficients.

Hint 2

Factor $α^{3} β^{3}$ out of the expression.

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: $α + β = - \frac{- 5}{1} = 5$
½ mark
Product of zeroes: $α β = \frac{3}{1} = 3$
½ mark
Take out the common factor: $α^{4} β^{3} + α^{3} β^{4} = α^{3} β^{3} (α + β) = (α β)^{3} (α + β)$
½ mark
$= 3^{3} \times 5 = 27 \times 5 = 135$
½ mark

Answer: 135

Where the marks are

$α + β = 5$ (½ mark)
$α β = 3$ (½ mark)
Writes the expression as $(α β)^{3} (α + β)$ (½ mark)
Value = 135 (½ 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 paper2025 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 24(b)

Hints

Step-by-step solution

Revise the chapter

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