If p(x) = x² − 7x + 12, what are the x-axis intersections of the graph?
Answer and explanation
Correct answer: (3, 0) and (4, 0)
An x-axis intersection occurs where p(x) = 0, so solve x² − 7x + 12 = 0. We factor the quadratic by finding two numbers whose product is 12 and whose sum is 7: 3 and 4. Thus x² − 7x + 12 = (x − 3)(x − 4). Setting each factor equal to zero gives x = 3 or x = 4. The corresponding graph points have y-coordinate zero, namely (3, 0) and (4, 0). Hence option A is correct. Option B has incorrect signs, option C gives y-axis points, and option D confuses the coefficients with the roots.
Frequently asked questions
What is the correct answer to this question?
(3, 0) and (4, 0)
Why is this the correct answer?
An x-axis intersection occurs where p(x) = 0, so solve x² − 7x + 12 = 0. We factor the quadratic by finding two numbers whose product is 12 and whose sum is 7: 3 and 4. Thus x² − 7x + 12 = (x − 3)(x − 4). Setting each factor equal to zero gives x = 3 or x = 4. The corresponding graph points have y-coordinate zero, namely (3, 0) and (4, 0). Hence option A is correct. Option B has incorrect signs, option C gives y-axis points, and option D confuses the coefficients with the 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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