At which x-values will the graph of the quadratic p(x)=x^2+2x-15 intersect the x-axis?
Answer and explanation
Correct answer: 3, -5
Set the quadratic equal to zero to find x-intercepts (roots).
Factor: \(x^2+2x-15=(x+5)(x-3)\).
Setting \((x+5)(x-3)=0\) gives x=-5 or x=3, so the graph meets the x-axis at x=3 and x=-5.
The closest distractor (-3, 5) is wrong because the signs of the roots are incorrect — the constant term -15 forces the product of roots to be -15, so one root must be negative.
Exam tip: Check constant term and middle coefficient quickly — product of roots = constant term, sum of roots = - (coefficient of x).
Frequently asked questions
What is the correct answer to this question?
3, -5
Why is this the correct answer?
Set the quadratic equal to zero to find x-intercepts (roots).
Factor: \(x^2+2x-15=(x+5)(x-3)\).
Setting \((x+5)(x-3)=0\) gives x=-5 or x=3, so the graph meets the x-axis at x=3 and x=-5.
The closest distractor (-3, 5) is wrong because the signs of the roots are incorrect — the constant term -15 forces the product of roots to be -15, so one root must be negative.
Exam tip: Check constant term and middle coefficient quickly — product of roots = constant term, sum of roots = - (coefficient of x).
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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