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Polynomials

Short Answer Type

61. Find the zero of the polynomial px + q + r.

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62. If p(x) = 5x³ - 2x² + 3x - 2, then find the values of p(1) and p(0). Also, find the value of p(-1).

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63. Determine whether the indicated numbers are zeroes of the given polynomial?

g(x) = 3x² - 2; $straight x equals fraction numerator 2 over denominator square root of 3 end fraction comma space minus fraction numerator 2 over denominator square root of 3 end fraction$

We have
g(x) = 3x² - 2

$8 open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses equals 3 open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses squared minus 2 equals 2 not equal to 0$

$therefore space space space space straight x space equals space fraction numerator 2 over denominator square root of 3 end fraction$ is not a zero of 8(x)

$8 open parentheses negative fraction numerator 2 over denominator square root of 3 end fraction close parentheses equals 3 open parentheses negative fraction numerator 2 over denominator square root of 3 end fraction close parentheses squared equals negative 2 not equal to 0$

$therefore space straight x equals space minus fraction numerator 2 over denominator square root of 3 end fraction$ is not a zero of 8(x).