If p(x)=(x-2)(x+6)^3, what are the distinct zeroes?
Answer and explanation
Correct answer: 2 and -6
The governing concept is that a zero is obtained by setting any factor of a factored polynomial equal to zero. From x-2=0, we get x=2. From (x+6)^3=0, we get x+6=0, so x=-6. The exponent 3 shows that -6 has multiplicity three, but multiplicity does not create three distinct zeroes. Consequently, the set of distinct zeroes is {2,-6}, so Option A is correct. Option C lists the repeated root three times and therefore gives multiplicities rather than distinct values. Option B changes both signs, and Option D incorrectly leaves out the zero coming from x-2.
Frequently asked questions
What is the correct answer to this question?
2 and -6
Why is this the correct answer?
The governing concept is that a zero is obtained by setting any factor of a factored polynomial equal to zero. From x-2=0, we get x=2. From (x+6)^3=0, we get x+6=0, so x=-6. The exponent 3 shows that -6 has multiplicity three, but multiplicity does not create three distinct zeroes. Consequently, the set of distinct zeroes is {2,-6}, so Option A is correct. Option C lists the repeated root three times and therefore gives multiplicities rather than distinct values. Option B changes both signs, and Option D incorrectly leaves out the zero coming from x-2.
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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