Standard form of a quadratic equation MCQs

Q1. A quadratic equation can have at most how many roots?

• A.infinitely many
• B.2
• C.1
• D.3

Answer: B. 2

Going back to the NCERT chapter, Apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation; substitute the coefficients and simplify => the radicand and the two roots reduce to clean values; so the required value = 2. That fits the listed correct option directly - Correct. Looking at the others: option A) 'infinitely many' fails since A non-zero quadratic has at most 2 roots; option C) '1' misses the point - It can have two distinct roots. Hence the answer is B) 2.

Q2. Which of these is a quadratic equation?

• A.x^3 - 1 = 0
• B.1/x + x = 2 written as 1 + x^2 = 2x is quadratic only after clearing - as written it is not in standard polynomial form
• C.2x + 3 = 0
• D.x^2 - 5x + 6 = 0

Answer: D. x^2 - 5x + 6 = 0

Q3. Which is NOT a quadratic equation?

• A.x(x - 2) = 5
• B.x^2 - 1 = 0
• C.3x^2 + x = 1
• D.x^2 = x^2 + 7x

Answer: D. x^2 = x^2 + 7x

Asked for the unknown; data is laid out in the stem. By apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation. apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation → so the required value = x^2 = x^2 + 7x. substitute the coefficients and simplify. Consequently option D) x^2 = x^2 + 7x. Others fail: option A) 'x(x - 2) = 5' fails since Expands to x^2 - 2x - 5 = 0, quadratic; option B) 'x^2 - 1 = 0' is incorrect: That is a genuine quadratic.