If the graph of p(x)=x^2+px+q cuts the x-axis at (-4,0) and (3,0), what will p and q be?
Answer and explanation
Correct answer: p=1, q=-12
The governing concept is the relationship between the zeroes and the factorised form of a monic quadratic. Since the graph meets the x-axis at x=-4 and x=3, these are the zeroes. Therefore p(x)=(x+4)(x-3). Expanding gives x^2-3x+4x-12=x^2+x-12. Comparing this with x^2+px+q, the coefficient of x is p=1 and the constant term is q=-12. Hence Option A is correct. Option B has the wrong sign for p, Option C uses the sum with an incorrect sign and the wrong constant sign, and Option D also has the wrong coefficient of x. The leading coefficient is 1, so no additional scaling is needed.
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What is the correct answer to this question?
p=1, q=-12
Why is this the correct answer?
The governing concept is the relationship between the zeroes and the factorised form of a monic quadratic. Since the graph meets the x-axis at x=-4 and x=3, these are the zeroes. Therefore p(x)=(x+4)(x-3). Expanding gives x^2-3x+4x-12=x^2+x-12. Comparing this with x^2+px+q, the coefficient of x is p=1 and the constant term is q=-12. Hence Option A is correct. Option B has the wrong sign for p, Option C uses the sum with an incorrect sign and the wrong constant sign, and Option D also has the wrong coefficient of x. The leading coefficient is 1, so no additional scaling is needed.
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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