Question

Which of the following graphs represents a polynomial with both zeroes being positive?

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

For a quadratic \(ax^2 + bx + c\) with both positive zeroes, the sum of roots (\(-b/a\)) must be positive and the product of roots (\(c/a\)) must also be positive.

Answer 1

The Correct Option is C

To determine which graph represents a polynomial with both zeroes being positive, let's review the properties of polynomial graphs, particularly quadratic polynomials.

• A quadratic polynomial is generally expressed as ax^2 + bx + c.
• The roots or zeroes of the polynomial are the values of x for which the polynomial equals zero.
• The graph of a quadratic polynomial is a parabola.
• If both roots are positive, the parabola must intersect the x-axis at two positive points.

Now, let's examine the images from the options:

This graph shows a parabola intersecting the x-axis at one positive and one negative point. Hence, it cannot be the correct graph.

In this graph, the parabola intersects the x-axis at two negative points, indicating both zeroes are negative. Therefore, it is not the correct graph.

This graph depicts a parabola intersecting the x-axis at two positive points. This satisfies the condition of having both zeroes being positive.

Here, the graph intersects the x-axis at one positive point and one negative point, so it cannot have two positive zeroes.

Based on the analysis, the graph with two positive zeroes is:

This is the correct answer as it shows a parabola intersecting the x-axis twice at positive values of x.