Find the value of k for which the roots of the quadratic equation 5x² - 10x + k = 0 are real and equal.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 23(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerQuadratic Equations

Find the value of k for which the roots of the quadratic equation $5 x^{2} - 10 x + k = 0$ are real and equal.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

What condition on the discriminant gives equal roots?

Hint 2

Set $b^{2} - 4 a c = 0$ with a = 5, b = −10, c = 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.

Comparing with $a x^{2} + b x + c = 0$ : $a = 5$ , $b = - 10$ , $c = k$ .
½ mark
For real and equal roots, discriminant $D = b^{2} - 4 a c = 0$ .
½ mark
$(- 10)^{2} - 4 (5) (k) = 0 \Rightarrow 100 - 20 k = 0$
½ mark
$k = 5$
½ mark

Answer: k = 5

Where the marks are

Identifies a, b, c (½ mark)
Uses condition $b^{2} - 4 a c = 0$ (½ mark)
Substitutes to get $100 - 20 k = 0$ (½ mark)
k = 5 (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Nature of Roots and Discriminant

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 23(a)

Hints

Step-by-step solution

Revise the chapter

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