Class 10 Graphical Meaning of Zeroes — practice questions with answers
Algebra — Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The zeroes of a polynomial p(x) are the x-coordinates of the points where the graph of y = p(x) meets which axis?
Ax-axis
By-axis
Cthe line y = x
Dthe origin only
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Answer: A) x-axis
A zero of p(x) is a value of x for which p(x) = 0, i.e. y = 0. Points with y = 0 lie on the x-axis, so zeroes are the x-coordinates of the points where the graph cuts the x-axis.
2. The graph of y = p(x) passes through the points where x = 0, x = 2 and x = -4 lie on the x-axis. The minimum possible degree of p(x) is:
A4
B3
C6
D2
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Answer: B) 3
There are 3 distinct zeroes (0, 2, -4), so the degree must be at least 3.
3. The graph of y = p(x) is a parabola with vertex on the x-axis. Its number of distinct real zeroes is:
A3
B2
C0
D1
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Answer: D) 1
If the vertex lies on the x-axis, the parabola touches it at exactly one point, giving one distinct (repeated) zero.
4. From the graph shown, count the number of zeroes of the polynomial.
A5
B3
C4
D8
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Answer: C) 4
The curve crosses the x-axis at four distinct points, so it has 4 zeroes.
5. A polynomial of degree 6 is graphed. It touches the x-axis at 2 distinct points and crosses it at 2 other distinct points, with no other intersections. How many real zeroes does it have counting multiplicity?
A7
B12
C5
D6
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Answer: D) 6
Each touch is a double zero: 2 touches give 2 x 2 = 4. Each crossing is a single zero: 2 crossings give 2. Total counting multiplicity = 4 + 2 = 6, matching degree 6.