Using quadratic formula, find the real roots of the equation 2x² + 2x + 9 = 0, if they exist.

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 28(a)

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section C, question 28(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(a) · 3 marks · Short answerQuadratic Equations

Using quadratic formula, find the real roots of the equation $2 x^{2} + 2 x + 9 = 0$ , if they exist.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

Before using the formula, work out b² − 4ac.

Hint 2

If the discriminant is negative, can its square root be real?

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.

Compare $2 x^{2} + 2 x + 9 = 0$ with $a x^{2} + b x + c = 0$ : $a = 2, b = 2, c = 9$ .
½ mark
Discriminant $D = b^{2} - 4 a c = 2^{2} - 4 (2) (9) = 4 - 72 = - 68$ .
1½ marks
By the quadratic formula $x = \frac{- b \pm D}{2 a}$ , but $- 68$ is not a real number. Since $D < 0$ , the equation has no real roots.
1 mark

Answer: D = −68 < 0, so no real roots exist.

Where the marks are

Identifies a, b, c and computes D = −68 (2 marks)
Concludes there are no real roots since D < 0 (1 mark)

Revise the chapter

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

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 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 28(a)

Hints

Step-by-step solution

Revise the chapter

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