If the graph of p(x) = x^2 + px + q cuts the x-axis at (-6, 0) and (2, 0), what will p and q be?
Answer and explanation
Correct answer: p = 4, q = -12
The x-intercepts give the zeroes of the monic quadratic: -6 and 2. A quadratic with these zeroes can be written as p(x) = (x + 6)(x - 2). Expanding gives x^2 - 2x + 6x - 12 = x^2 + 4x - 12. Comparing this with the standard form x^2 + px + q, the coefficient of x is p = 4 and the constant term is q = -12. Therefore option A is correct. The sum of the zeroes is -4, which equals -p, so p must be 4; confusing the sum directly with p leads to option B. The product is -12, not 12, ruling out option C, and option D has an incorrect coefficient.
Frequently asked questions
What is the correct answer to this question?
p = 4, q = -12
Why is this the correct answer?
The x-intercepts give the zeroes of the monic quadratic: -6 and 2. A quadratic with these zeroes can be written as p(x) = (x + 6)(x - 2). Expanding gives x^2 - 2x + 6x - 12 = x^2 + 4x - 12. Comparing this with the standard form x^2 + px + q, the coefficient of x is p = 4 and the constant term is q = -12. Therefore option A is correct. The sum of the zeroes is -4, which equals -p, so p must be 4; confusing the sum directly with p leads to option B. The product is -12, not 12, ruling out option C, and option D has an incorrect coefficient.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
