If p(x)=9x^2-16, what are the x-axis intersections (x-intercepts) of its graph?
Answer and explanation
Correct answer: \(\left(\frac{4}{3},0\right)\) and \(\left(-\frac{4}{3},0\right)\)
Set p(x)=0 to find x-intercepts: 9x^2-16=0 ⇒ 9x^2=16 ⇒ x^2=16/9 ⇒ x=±4/3. Alternatively factor as a difference of squares: 9x^2-16=(3x-4)(3x+4), giving x=4/3 and x=-4/3. Distractor C (±3/4) is the reciprocal mistake; B (±4) would be from x^2-16=0. Exam tip: either factor as (3x-4)(3x+4) or take square roots after isolating x^2 to avoid arithmetic slips.
Frequently asked questions
What is the correct answer to this question?
\(\left(\frac{4}{3},0\right)\) and \(\left(-\frac{4}{3},0\right)\)
Why is this the correct answer?
Set p(x)=0 to find x-intercepts: 9x^2-16=0 ⇒ 9x^2=16 ⇒ x^2=16/9 ⇒ x=±4/3. Alternatively factor as a difference of squares: 9x^2-16=(3x-4)(3x+4), giving x=4/3 and x=-4/3. Distractor C (±3/4) is the reciprocal mistake; B (±4) would be from x^2-16=0. Exam tip: either factor as (3x-4)(3x+4) or take square roots after isolating x^2 to avoid arithmetic slips.
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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