If x = -2 is the root of the equation  and is also the zero of

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 Multiple Choice QuestionsShort 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
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64. Determine whether the indicated numbers are zeroes of the given polynomial?

f(x) = x- 6x+ 11x - 6;   x = 1, 3
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65. Find the value of the polynomial straight p left parenthesis straight z right parenthesis equals 3 straight z squared minus 4 straight z plus square root of 17 when z =3.

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66. If x = -2 is the root of the equation square root of 5 space left parenthesis x plus p right parenthesis equals 0 and is also the zero of the polynomial px squared plus kx plus 2 square root of 2 comma then find the value of k.


space space space space square root of 2 left parenthesis x plus p right parenthesis equals 0
rightwards double arrow space space x plus p space equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space vertical line space because space square root of 2 not equal to 0
rightwards double arrow space x space equals space minus p
According to the question.

                        - p = - 2
rightwards double arrow space space space space                   p = 2
Let     f(x) = px+ kx + 2 square root of 2

Then,   f(x) = 2x+ kx + 2 square root of 2
If x = -2 is a zero of f(x), then f(-2) = 0

rightwards double arrow space space space space space 2 left parenthesis negative 2 right parenthesis squared space plus space straight k left parenthesis negative 2 right parenthesis space plus space 2 square root of 2 space equals space 0
rightwards double arrow space space space space 2 straight k space equals space 8 space plus space 2 square root of 2
rightwards double arrow space space space space space straight k space equals space 4 plus square root of 2
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67. Find the value of each of the following polynomials at the indicated value of variables:

p(x) = 5x2 - 3x + 7 at x = 1



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68. Find the value of each of the following polynomials at the indicated value of variables:

q(y) = 3y3 - 4y + square root of 11 at y = 2



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69. Find the value of each of the following polynomials at the indicated value of variables:

p(t) = 4t4 + 5t- t2 + 6 at t = a



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70.  Check whether - 2 and 2 are zeroes of the polynomial x + 2.
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