Question

3 square root of, 3, end square root is a zero of a polynomial p(x)p(x)p, left parenthesis, x, right parenthesis. Find the value of \sqrt3\cdot{p(\sqrt3)} 3 p( 3 )square root of, 3, end square root, dot, p, left parenthesis, square root of, 3, end square root, right parenthesis

Answer 1

Polynomials

Given: √3 is a zero of a polynomial p(x)

To find: the value of p(√3)

Solution:

• We must understand that since √3 is a zero of p(x), the value x = √3 satisfies the equation p(x) = 0

• i.e., p(√3) = 0

Answer: the value of p(√3) is 0.

Note:

• The problem can be solved in another way.

• Since √3 is an irrational number, the other zero of p(x) will be - √3.

• Now find the polynomial p(x) = r(x) (x - √3) (x + √3), where r(x) is a polynomial.

• Put x = √3 and you will get p(√3) = 0.

Answer 2

Answer:

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