If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and -3, then find the values of a and b.

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 23

From the official CBSE sample question paper for 2025-26, 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 the zeroes of the quadratic polynomial $x^{2} + (a + 1) x + b$ are 2 and $- 3$ , then find the values of $a$ and $b$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Recall the relations between zeroes and coefficients of $a x^{2} + b x + c$ .

Hint 2

Sum of zeroes $= - \frac{coeff of x}{coeff of x ^{2}}$ and product $= \frac{constant}{coeff of x ^{2}}$ .

Step-by-step solution

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For $x^{2} + (a + 1) x + b$ : sum of zeroes $= - \frac{a + 1}{1}$ . So $2 + (- 3) = - (a + 1) \Rightarrow - 1 = - (a + 1) \Rightarrow a = 0$
1 mark
Product of zeroes $= \frac{b}{1}$ . So $2 \times (- 3) = b \Rightarrow b = - 6$ . Hence $a = 0, b = - 6$ .
1 mark

Answer: $a = 0, b = - 6$

Where the marks are

Uses sum of zeroes to get $a = 0$ (1 mark)
Uses product of zeroes to get $b = - 6$ (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 paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 23

Hints

Step-by-step solution

Revise the chapter

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