Which of the following quadratic equations has sum of its roots as 4 ? (A) 2x²-4x+8=0 (B) -x²+4x+4=0 (C) √(2)x²-(4)/(√(2))x+1=0 (D) 4x²-4x+4=0

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 1

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQQuadratic Equations

Which of the following quadratic equations has sum of its roots as $4$ ?

(A) $2 x^{2} - 4 x + 8 = 0$
(B) $- x^{2} + 4 x + 4 = 0$
(C) $2 x^{2} - \frac{4}{2} x + 1 = 0$
(D) $4 x^{2} - 4 x + 4 = 0$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Recall the relation between coefficients and the sum of roots.

Hint 2

Compute $- b / a$ for each option, watching the sign of $a$ .

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.

For $a x^{2} + b x + c = 0$ , sum of roots $= - \frac{b}{a}$ .
(A) $\frac{4}{2} = 2$ ; (B) $- \frac{4}{- 1} = 4$ ; (C) $\frac{4/ 2}{2} = 2$ ; (D) $\frac{4}{4} = 1$ . Only (B) gives 4.
1 mark

Answer: Option (B) $- x^{2} + 4 x + 4 = 0$

Where the marks are

Uses sum $= - b / a$ and picks (B) (1 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 paper2023 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 1

Hints

Step-by-step solution

Revise the chapter

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