The zeroes of a polynomial x²+px+q are twice the zeroes of the polynomial 4x²-5x-6. The value of p is: (A) -5/2 (B) 5/2 (C) -5 (D) 10

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 10

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

Q10 · 1 mark · MCQPolynomials

The zeroes of a polynomial $x^{2} + p x + q$ are twice the zeroes of the polynomial $4 x^{2} - 5 x - 6$ . The value of $p$ is:

(A) $- \frac{5}{2}$
(B) $\frac{5}{2}$
(C) $- 5$
(D)10

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

Hints

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

Hint 1

Find the sum of zeroes of $4 x^{2} - 5 x - 6$ .

Hint 2

The new zeroes are doubled, so their sum doubles; the sum of zeroes of $x^{2} + p x + q$ is $- p$ .

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.

For $4 x^{2} - 5 x - 6$ , the sum of zeroes is $α + β = \frac{5}{4}$ .
The zeroes of $x^{2} + p x + q$ are $2 α$ and $2 β$ , so their sum is $\frac{5}{2} = - p$ . Hence $p = - \frac{5}{2}$ . The answer is option (A).
1 mark

Answer: $p = - \frac{5}{2}$ , option (A)

Where the marks are

Doubles the sum of zeroes and equates it to $- p$ , giving $p = - \frac{5}{2}$ , option (A) (1 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 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 10

Hints

Step-by-step solution

Revise the chapter

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