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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.

If $space straight p left parenthesis straight x right parenthesis space equals space 6 straight x to the power of 4 plus 8 straight x cubed minus 5 straight x squared plus ax plus straight b space straight q left parenthesis straight x right parenthesis space equals space 2 straight x squared space minus space 5$
If Now, and
Now,
$20 straight x plus ax plus straight b minus 25 equals 0 straight x left parenthesis 20 plus straight a right parenthesis plus straight b minus 25 equals 0. straight x plus 0 rightwards double arrow space space space space space space space space space straight a space plus space 20 space equals space 0$

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$rightwards double arrow$ $straight a equals negative 20$
and $straight b equals 25$
Hence, other zeroes are -20, 25.