Geometric meaning of zeros of a polynomial MCQs

Q1. The graph of y = x^2 + 1 has how many real zeros?

• A.2
• B.0
• C.1
• D.infinitely many

Answer: B. 0

Q2. Which cannot be the number of real zeros of a quadratic polynomial?

• A.2
• B.0
• C.1
• D.3

Answer: D. 3

Spot-the-setup - a typical math numerical. We are after the quantity the stem asks for. Tool of choice - apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation. Rearrange it for the unknown before substituting. Numbers in: apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation → so the required value = 3. Common-sense check: substitute the coefficients and simplify. Lock in option D) 3. Trap-watch: option A) '2' is wrong because Possible: graph cuts the x-axis twice; option B) '0' is incorrect: Possible: graph misses the x-axis.

Q3. In an archery target overlay, the arrow's path outline meets the ground line at 1 unique points; how many real zeros does the path polynomial possess?

• A.2
• B.3
• C.0
• D.1

Answer: D. 1

Real zeros are precisely the x-values where the graph meets the horizontal axis (there the polynomial equals 0). The curve meets the axis at 1 distinct points, so it has 1 real zeros.