If one zero of the quadratic polynomial 2x² - 3x + p is 3, find the value of p. Also, find the other zero.

MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 23

From the official CBSE sample question paper for 2026-27, 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 one zero of the quadratic polynomial $2 x^{2} - 3 x + p$ is 3, find the value of $p$ . Also, find the other zero.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

If 3 is a zero, what is the value of the polynomial at $x = 3$ ?

Hint 2

After finding $p$ , use the sum (or product) of zeroes to get the other zero.

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.

Since 3 is a zero, $p (3) = 0$ : $2 (3)^{2} - 3 (3) + p = 0$
½ mark
$18 - 9 + p = 0 \Rightarrow p = - 9$
½ mark
Let the other zero be $β$ . Sum of zeroes $= - \frac{b}{a}$ , so $3 + β = \frac{- ( - 3 )}{2} = \frac{3}{2}$
½ mark
$β = \frac{3}{2} - 3 = - \frac{3}{2}$
½ mark

Answer: $p = - 9$ ; other zero $= - \frac{3}{2}$

Where the marks are

Substitutes $x = 3$ and equates to 0 (½ mark)
Gets $p = - 9$ (½ mark)
Uses sum of zeroes $= - b / a$ (½ mark)
Other zero $= - \frac{3}{2}$ (½ 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 paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 23

Hints

Step-by-step solution

Revise the chapter

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