If the graph of p(x) = x² + px + q cuts the x-axis at (−8, 0) and (5, 0), what are p and q?
Answer and explanation
Correct answer: p = 3, q = −40
The x-coordinates of the x-axis intersections are the zeroes of the polynomial, so the zeroes are −8 and 5. Since the coefficient of x² is 1, the polynomial can be written as (x + 8)(x − 5). Expanding gives x² − 5x + 8x − 40 = x² + 3x − 40. Comparing this with x² + px + q, we obtain p = 3 and q = −40. Therefore option A is correct. The sign of p is positive because the middle terms combine to +3x, while q is negative because the product of the zeroes is −40.
Frequently asked questions
What is the correct answer to this question?
p = 3, q = −40
Why is this the correct answer?
The x-coordinates of the x-axis intersections are the zeroes of the polynomial, so the zeroes are −8 and 5. Since the coefficient of x² is 1, the polynomial can be written as (x + 8)(x − 5). Expanding gives x² − 5x + 8x − 40 = x² + 3x − 40. Comparing this with x² + px + q, we obtain p = 3 and q = −40. Therefore option A is correct. The sign of p is positive because the middle terms combine to +3x, while q is negative because the product of the zeroes is −40.
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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