If the graph of p(x) = x^2 + px + q cuts the x-axis at (-9, 0) and (4, 0), what will p and q be?
Answer and explanation
Correct answer: p = 5, q = -36
The x-axis intersections are the zeroes, so the roots are -9 and 4. Since the coefficient of x^2 is 1, construct the polynomial as (x + 9)(x - 4). Expanding gives x^2 - 4x + 9x - 36 = x^2 + 5x - 36. Comparing with x^2 + px + q gives p = 5 and q = -36. Hence option A is correct. The sum of the roots is -5, equal to -p, so using it directly as p produces option B. Their product is -36, not +36, ruling out option C. Option D has both an incorrect x-coefficient and an incorrect sign for p.
Frequently asked questions
What is the correct answer to this question?
p = 5, q = -36
Why is this the correct answer?
The x-axis intersections are the zeroes, so the roots are -9 and 4. Since the coefficient of x^2 is 1, construct the polynomial as (x + 9)(x - 4). Expanding gives x^2 - 4x + 9x - 36 = x^2 + 5x - 36. Comparing with x^2 + px + q gives p = 5 and q = -36. Hence option A is correct. The sum of the roots is -5, equal to -p, so using it directly as p produces option B. Their product is -36, not +36, ruling out option C. Option D has both an incorrect x-coefficient and an incorrect sign for p.
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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