If p(x) = x² − 3x − 10, what are the x-axis intersections of the graph?
Answer and explanation
Correct answer: (5, 0) and (−2, 0)
The governing concept is that x-axis intersections occur where p(x) = 0, and their coordinates are (zero, 0). Factor the polynomial: x² − 3x − 10 = (x − 5)(x + 2), because the two numbers 5 and −2 have product −10 and sum −3. Setting each factor equal to zero gives x − 5 = 0, so x = 5, and x + 2 = 0, so x = −2. Consequently, the graph intersects the x-axis at (5, 0) and (−2, 0), making option A correct. Option B reverses both signs, option C gives y-axis points rather than x-axis points, and option D incorrectly uses the constant and linear coefficients as roots.
Frequently asked questions
What is the correct answer to this question?
(5, 0) and (−2, 0)
Why is this the correct answer?
The governing concept is that x-axis intersections occur where p(x) = 0, and their coordinates are (zero, 0). Factor the polynomial: x² − 3x − 10 = (x − 5)(x + 2), because the two numbers 5 and −2 have product −10 and sum −3. Setting each factor equal to zero gives x − 5 = 0, so x = 5, and x + 2 = 0, so x = −2. Consequently, the graph intersects the x-axis at (5, 0) and (−2, 0), making option A correct. Option B reverses both signs, option C gives y-axis points rather than x-axis points, and option D incorrectly uses the constant and linear coefficients as roots.
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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