If p(x) = (x - 4)(x + 7)^3, what are the distinct zeroes?
Answer and explanation
Correct answer: 4 and -7
A zero is obtained by setting any factor equal to zero. From x - 4 = 0, we get x = 4. From (x + 7)^3 = 0, we get x + 7 = 0, so x = -7. The exponent 3 tells us that -7 has multiplicity three, meaning it is repeated as a root, but it remains only one distinct zero. Therefore the set of distinct zeroes is {4, -7}, so option A is correct. Option C lists the repeated root several times and therefore describes multiplicity rather than distinct values. Option B changes both signs, while option D incorrectly omits the zero arising from x - 4.
Frequently asked questions
What is the correct answer to this question?
4 and -7
Why is this the correct answer?
A zero is obtained by setting any factor equal to zero. From x - 4 = 0, we get x = 4. From (x + 7)^3 = 0, we get x + 7 = 0, so x = -7. The exponent 3 tells us that -7 has multiplicity three, meaning it is repeated as a root, but it remains only one distinct zero. Therefore the set of distinct zeroes is {4, -7}, so option A is correct. Option C lists the repeated root several times and therefore describes multiplicity rather than distinct values. Option B changes both signs, while option D incorrectly omits the zero arising from x - 4.
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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