If one zero of the quadratic polynomial 6x² + 37x - (p - 2) is reciprocal of the other, then find the value of p.

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 25(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section B, question 25(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(b) · 2 marks · Very short answerPolynomials

If one zero of the quadratic polynomial $6 x^{2} + 37 x - (p - 2)$ is reciprocal of the other, then find the value of p.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

If one zero is the reciprocal of the other, what is their product?

Hint 2

Product of zeroes $= \frac{c}{a}$ ; be careful with the sign of $c = - (p - 2)$ .

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.

Here $a = 6$ , $b = 37$ , $c = - (p - 2)$ . Let the zeroes be $α$ and $\frac{1}{α}$ .
½ mark
Product of zeroes $= α \times \frac{1}{α} = \frac{c}{a} \Rightarrow 1 = \frac{- ( p - 2 )}{6}$
1 mark
$6 = - p + 2 \Rightarrow p = - 4$
½ mark

Answer: p = −4

Where the marks are

Takes zeroes as $α, \frac{1}{α}$ (½ mark)
Equates product $1 = \frac{- ( p - 2 )}{6}$ (1 mark)
Gets $p = - 4$ (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 paper2024 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 25(b)

Hints

Step-by-step solution

Revise the chapter

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