If p(x)=5x^2-5, what are its zeroes and their type?
Answer and explanation
Correct answer: (1, -1), rational
A zero of a polynomial is a value of x for which the polynomial becomes zero. Set 5x²−5=0. Factoring gives 5(x²−1)=0, so x²−1=0 and therefore (x−1)(x+1)=0. Hence x=1 or x=−1. Both numbers are integers, and every integer is rational because it can be written as a quotient of two integers, such as 1=1/1 and −1=−1/1. The common factor 5 does not produce √5; it is removed by division. Thus option A is correct. Option C confuses coefficients with roots, option B results from an incorrect rearrangement, and option D is false because two real roots exist.
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What is the correct answer to this question?
(1, -1), rational
Why is this the correct answer?
A zero of a polynomial is a value of x for which the polynomial becomes zero. Set 5x²−5=0. Factoring gives 5(x²−1)=0, so x²−1=0 and therefore (x−1)(x+1)=0. Hence x=1 or x=−1. Both numbers are integers, and every integer is rational because it can be written as a quotient of two integers, such as 1=1/1 and −1=−1/1. The common factor 5 does not produce √5; it is removed by division. Thus option A is correct. Option C confuses coefficients with roots, option B results from an incorrect rearrangement, and option D is false because two real roots exist.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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