If 2/3 is a root of the quadratic equation kx² - x - 2 = 0, then find the value of k.

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

CBSE Class 10 Mathematics Basic 2024: question 23

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, 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 answerQuadratic Equations

If $\frac{2}{3}$ is a root of the quadratic equation $k x^{2} - x - 2 = 0$ , then find the value of k.

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

A root of an equation makes it true when substituted for $x$ .

Hint 2

Put $x = \frac{2}{3}$ and solve the resulting linear equation in $k$ .

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.

Since $\frac{2}{3}$ is a root, it satisfies the equation:
$k (\frac{2}{3})^{2} - \frac{2}{3} - 2 = 0$
½ mark
$\frac{4}{9} k = \frac{2}{3} + 2 = \frac{8}{3}$
1 mark
$k = \frac{8}{3} \times \frac{9}{4} = 6$
½ mark

Answer: k = 6

Where the marks are

Substitutes $x = \frac{2}{3}$ in the equation (½ mark)
Obtains $\frac{4}{9} k = \frac{8}{3}$ (1 mark)
Gets $k = 6$ (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Quadratic Equations, 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 23

Hints

Step-by-step solution

Revise the chapter

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