One zero of the polynomial 4x² – 12x + (2k + 1) is five times the other. Find the value of k.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerPolynomials

One zero of the polynomial $4 x^{2} -12 x + (2 k + 1)$ is five times the other. Find the value of k.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Call the smaller zero $α$ ; what is the other zero?

Hint 2

Use the sum of zeroes $= - \frac{b}{a}$ to find $α$ .

Hint 3

Then use the product of zeroes $= \frac{c}{a}$ to find k.

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.

Let the zeroes be $α$ and $5 α$ .
½ mark
Sum of zeroes: $α + 5 α = \frac{12}{4} = 3 \Rightarrow 6 α = 3 \Rightarrow α = \frac{1}{2}$
½ mark
Product of zeroes: $α \times 5 α = \frac{2 k + 1}{4} \Rightarrow 5 \cdot \frac{1}{4} = \frac{2 k + 1}{4}$
½ mark
$\Rightarrow 2 k + 1 = 5 \Rightarrow k = 2$
½ mark

Answer: $k = 2$

Where the marks are

Takes zeroes as $α$ and $5 α$ (½ mark)
Uses sum of zeroes to get $α = \frac{1}{2}$ (½ mark)
Writes product $5 α^{2} = \frac{2 k + 1}{4}$ (½ mark)
Obtains $k = 2$ (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 paper2026 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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