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Polynomials

Long Answer Type

441. Find all the zeros of the polynomial 2x⁴ + 7x³ – 19x² – 14x + 30, if two of its zeros are

square root of 2 space and space minus square root of 2

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Short Answer Type

442. What real number should be subtracted from the polynomial 3x² + 10x²– 14x + 9, so that the polynomial 3x– 2 divides it exactly ?

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Long Answer Type

443.

Find all other zeroes of $straight x to the power of 4 plus straight x cubed minus 23 straight x squared minus 3 straight x plus 60 comma$ if it is given that two of its zeroes are $square root of 3 space and space minus square root of 3.$

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444. If the polynomial 6x⁴ + 8x³ – 5x² + ax + b is exactly divisible by the polynomial 2x² – 5, then find the values of a and b.

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445. Find all the zeroes of the polynomial

negative 2 square root of 2 straight x cubed minus 18 straight x squared plus 24 square root of 2 straight x plus 72

given that

2 square root of 3 space straight x to the power of 4 space and space minus 2 square root of 3

are two of its zeroes.

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Short Answer Type

446.

Draw the graph of y = x²–x and find the zeroes.

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447. Draw the graph of the quadratic polynomial y = x² – 1. Find the zeroes from the graph.

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448. Draw the graph of the cubic polynomial y = x³ – 1. Find the zeroes from the graph.

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449. Draw the graph of the linear polynomial y = 2x. Find the zeroes from the graph.

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450. Draw the graph of the linear equation y = 6 - 2x. Find the zeroes from the graph.

Solution not provided.

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