If the graph of a quadratic polynomial cuts the x-axis at (-2, 0) and (7, 0), what are the values of p(-2) and p(7)?
Answer and explanation
Correct answer: Both are 0
The graph of y = p(x) intersects the x-axis at a point whose y-coordinate is zero. At (-2, 0), the y-coordinate gives p(-2) = 0. Similarly, at (7, 0), the y-coordinate gives p(7) = 0. Therefore both values are zero, and -2 and 7 are the two zeroes of the quadratic polynomial. The signs of the polynomial between or outside the zeroes do not change these endpoint values.
Frequently asked questions
What is the correct answer to this question?
Both are 0
Why is this the correct answer?
The graph of y = p(x) intersects the x-axis at a point whose y-coordinate is zero. At (-2, 0), the y-coordinate gives p(-2) = 0. Similarly, at (7, 0), the y-coordinate gives p(7) = 0. Therefore both values are zero, and -2 and 7 are the two zeroes of the quadratic polynomial. The signs of the polynomial between or outside the zeroes do not change these endpoint values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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