If p(-6)=0, p(-1)>0, p(4)=0 and p(7)<0, what is the product of the given zeroes?
Answer and explanation
Correct answer: -24
A zero of p(x) is an input x for which p(x)=0. From the information given, p(-6)=0 and p(4)=0, so the stated zeroes are -6 and 4. The values p(-1)>0 and p(7)<0 are sign information, not additional zeroes, because neither value equals zero. Their product is (-6)(4)=-24. Therefore Option A is correct. Option B loses the negative sign, Option C incorrectly multiplies or combines the two x-values as a difference, and Option D would be possible only if one of the zeroes were 0. The inequalities help describe signs near the roots but do not change the requested product.
Frequently asked questions
What is the correct answer to this question?
-24
Why is this the correct answer?
A zero of p(x) is an input x for which p(x)=0. From the information given, p(-6)=0 and p(4)=0, so the stated zeroes are -6 and 4. The values p(-1)>0 and p(7)<0 are sign information, not additional zeroes, because neither value equals zero. Their product is (-6)(4)=-24. Therefore Option A is correct. Option B loses the negative sign, Option C incorrectly multiplies or combines the two x-values as a difference, and Option D would be possible only if one of the zeroes were 0. The inequalities help describe signs near the roots but do not change the requested product.
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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