Assertion (A): If one root of the quadratic equation 4x² - 10x + (k - 4) = 0 is reciprocal of the other, then value of k is 8. Reason (R): Roots of the quadratic equation x² - x + 1 = 0 are real. (A) Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true but Reason (R) does not give the correct explanation of Assertion (A). (C) Assertion (A) is true but Reason (R) is false. (D) Assertion (A) is false but Reason (R) is true.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2023: question 20

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedQuadratic Equations

Assertion (A): If one root of the quadratic equation $4 x^{2} - 10 x + (k - 4) = 0$ is reciprocal of the other, then value of $k$ is $8$ .

Reason (R): Roots of the quadratic equation $x^{2} - x + 1 = 0$ are real.

(A)Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true but Reason (R) does not give the correct explanation of Assertion (A).
(C)Assertion (A) is true but Reason (R) is false.
(D)Assertion (A) is false but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

What is the product of a number and its reciprocal?

Hint 2

For R, find the discriminant of $x^{2} - x + 1 = 0$ and check its sign.

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.

If the roots are reciprocals, their product is 1, so $\frac{k - 4}{4} = 1$ , giving $k = 8$ . A is true.
For $x^{2} - x + 1 = 0$ : $D = 1 - 4 = - 3 < 0$ , so the roots are not real and R is false. Answer: option (C).
1 mark

Answer: Option (C)

Where the marks are

Shows $k = 8$ using product of roots = 1, and $D < 0$ for R (1 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 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 20

Hints

Step-by-step solution

Revise the chapter

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