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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

3131 Views

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 ?

134 Views

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 $square root of 3 space and space minus square root of 3.$

113 Views

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.

243 Views

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.

Since two zeroes are $2 square root of 3 space and space minus 2 square root of 3$
$rightwards double arrow$ $left parenthesis straight x minus 2 square root of 3 right parenthesis space left parenthesis straight x plus 2 square root of 3 right parenthesis space equals space straight x squared minus 12$ is a factor of the given polynomial.
Now,
Since two zeroes are is a factor of the given polynomia
Now, $straight x to the power of 4 minus 2 square root of 2 straight x cubed minus 18 straight x squared plus 24 square root of 2 straight x plus 72$
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$equals left parenthesis straight x plus 2 square root of 3 right parenthesis space left parenthesis straight x minus 2 square root of 3 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets straight x left parenthesis straight x minus 3 square root of 2 right parenthesis space plus space square root of 2 left parenthesis straight x minus 3 square root of 2 right parenthesis close square brackets$

= $left parenthesis straight x plus 2 square root of 3 right parenthesis space left parenthesis straight x minus 2 square root of 3 right parenthesis space left parenthesis straight x plus square root of 2 right parenthesis space left parenthesis straight x minus 3 square root of 2 right parenthesis$
Hence, other zeroes are
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