Question:
Observe the graph of polynomial p(x). The zeroes of the polynomial are
Observe the graph of polynomial p(x). The zeroes of the polynomial are
Show Hint
A common error is to include the y-intercept (such as \(0\) from \((0, 4)\)) as one of the zeroes.
Remember, zeroes are only the \(x\)-coordinates of points on the horizontal axis (where \(y = 0\)).
Always double-check that you are only reading values off the horizontal \(x\)-axis!
Remember, zeroes are only the \(x\)-coordinates of points on the horizontal axis (where \(y = 0\)).
Always double-check that you are only reading values off the horizontal \(x\)-axis!
Updated On: Jul 22, 2026
- –2, 0, 2.5
- –2, 2.5
- 0, 4
- –2, 0
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
The topic of this question is Polynomials, specifically focusing on identifying their zeroes from a graph.
The zeroes of a polynomial \(p(x)\) are the values of \(x\) for which \(p(x) = 0\).
When we plot the graph of \(y = p(x)\) on a coordinate plane, the zeroes are the \(x\)-coordinates of the points where the graph intersects or touches the horizontal \(x\)-axis.
Step 2: Key Formula or Approach:
To find the zeroes from the graph:
- Look at the horizontal \(x\)-axis.
- Identify the coordinates of the points where the curve crosses or touches the \(x\)-axis.
- Ignore any y-intercepts (where the curve crosses the y-axis, like the point \((0, 4)\)), as they do not represent zeroes of \(p(x)\).
Step 3: Detailed Explanation:
• Let us analyze the given graph of the polynomial \(y = p(x)\):
The curve is a parabola opening downwards, representing a quadratic polynomial.
• Identify the points on the axes labeled in the diagram:
- The point on the y-axis is \((0, 4)\). This is the y-intercept, not a zero of the polynomial.
- The points on the horizontal \(x\)-axis are \((-2, 0)\) and \((2.5, 0)\).
• Determine the zeroes from the x-intercepts:
The curve intersects the \(x\)-axis at \(x = -2\) and \(x = 2.5\).
Therefore, the zeroes of the polynomial are \(-2\) and \(2.5\).
Step 4: Final Answer:
The zeroes of the polynomial \(p(x)\) are \(-2\) and \(2.5\).
Therefore, the correct option is (B).
The topic of this question is Polynomials, specifically focusing on identifying their zeroes from a graph.
The zeroes of a polynomial \(p(x)\) are the values of \(x\) for which \(p(x) = 0\).
When we plot the graph of \(y = p(x)\) on a coordinate plane, the zeroes are the \(x\)-coordinates of the points where the graph intersects or touches the horizontal \(x\)-axis.
Step 2: Key Formula or Approach:
To find the zeroes from the graph:
- Look at the horizontal \(x\)-axis.
- Identify the coordinates of the points where the curve crosses or touches the \(x\)-axis.
- Ignore any y-intercepts (where the curve crosses the y-axis, like the point \((0, 4)\)), as they do not represent zeroes of \(p(x)\).
Step 3: Detailed Explanation:
• Let us analyze the given graph of the polynomial \(y = p(x)\):
The curve is a parabola opening downwards, representing a quadratic polynomial.
• Identify the points on the axes labeled in the diagram:
- The point on the y-axis is \((0, 4)\). This is the y-intercept, not a zero of the polynomial.
- The points on the horizontal \(x\)-axis are \((-2, 0)\) and \((2.5, 0)\).
• Determine the zeroes from the x-intercepts:
The curve intersects the \(x\)-axis at \(x = -2\) and \(x = 2.5\).
Therefore, the zeroes of the polynomial are \(-2\) and \(2.5\).
Step 4: Final Answer:
The zeroes of the polynomial \(p(x)\) are \(-2\) and \(2.5\).
Therefore, the correct option is (B).
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