Find all the zeros of the polynomial 2x4 + 7x3 – 19x2 – 1

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 Multiple Choice QuestionsLong Answer Type

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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


Since, two zeros are square root of 2 space and space square root of 2 comma
∴  left parenthesis straight x minus square root of 2 right parenthesis space left parenthesis straight x plus square root of 2 right parenthesis space equals space straight x squared minus 2 is a factor of the given polynomial.
Now, we divide the given polynomial by x2 – 2.

Since, two zeros are ∴   is a factor of the given polynomial.Now
∴  2 straight x to the power of 4 plus 7 straight x cubed minus 19 straight x squared minus 14 straight x plus 30 space equals space left parenthesis straight x squared minus 2 right parenthesis space left parenthesis 2 straight x squared plus 7 straight x minus 15 right parenthesis

Now,2x2 + 7x – 15
= 2x2 + 10x –3x – 15
= 2y (x + 5) – 3 (x + 5) = (x + 5) (2x – 3)
So. its zeros are given by x = – 5 and x = 3/2 . Hence, the zeros of the given polynomials are :
square root of 2 comma space left parenthesis negative square root of 2 right parenthesis comma space left parenthesis negative 5 right parenthesis space and space 3 over 2   Ans. 
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 Multiple Choice QuestionsShort Answer Type

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 Multiple Choice QuestionsLong Answer Type

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 Multiple Choice QuestionsShort Answer Type

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