If p(x)=(x−2)(x+3), which zeros will appear on the number line?
Answer and explanation
Correct answer: 2 and −3
Answer: C, 2 and −3. A zero of p(x) is an x-value for which p(x)=0. The polynomial is already factorised, so use the zero-product property: a product is zero when at least one factor is zero. Set x−2=0, giving x=2. Set x+3=0, giving x=−3. These are the x-intercepts, or the points where the graph meets the x-axis; they can therefore be marked at 2 and −3 on the number line. Checking gives p(2)=0×5=0 and p(−3)=−5×0=0. A changes −3 to +3, B changes 2 to −2, and D changes both signs incorrectly. The sign warning is important: x−a gives zero a, while x+a gives zero −a.
Frequently asked questions
What is the correct answer to this question?
2 and −3
Why is this the correct answer?
Answer: C, 2 and −3. A zero of p(x) is an x-value for which p(x)=0. The polynomial is already factorised, so use the zero-product property: a product is zero when at least one factor is zero. Set x−2=0, giving x=2. Set x+3=0, giving x=−3. These are the x-intercepts, or the points where the graph meets the x-axis; they can therefore be marked at 2 and −3 on the number line. Checking gives p(2)=0×5=0 and p(−3)=−5×0=0. A changes −3 to +3, B changes 2 to −2, and D changes both signs incorrectly. The sign warning is important: x−a gives zero a, while x+a gives zero −a.
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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