Find all the other zeros 2x4 3x3 5x2 9x 3 it being given that two of its zeros are 3 3

Find all the zeroes of 2x4 3x3 5x2 + 9x 3, if two of its zeroes are √3 and √3.

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find all the zeros of 2x4-3x3-5x2+9x-3 if it is given that two of its zeroes are root3 and root -3

Posted by Vanshjeet Sodhi 3 years ago

Product of zeroes is -9 then EW. Is. x2-9 . Now divide the equation. By x2-9 . REDULT equal to zero and find the two new zeries

The given polynomial is f(x) = `2x^4 – 3x^3 – 5x^2 + 9x – 3`Since √3 and –√3 are the zeroes of f(x), it follows that each one of `(x – sqrt3) `and `(x + sqrt3)`is a factor of f(x).Consequently, `(x – sqrt3) (x + sqrt3)` = (x2 – 3) is a factor of f(x).

On dividing f(x) by (x2 – 3), we get:  

`f(x) = 0``⇒ 2x^4 – 3x^3 – 5x2 + 9x – 3 = 0``⇒ (x^2 – 3) (2x^2– 3x + 1) = 0``⇒ (x^2 – 3) (2x2– 2x – x + 1) = 0``⇒ (x – sqrt3) (x + sqrt3) (2x – 1) (x – 1) = 0``⇒ x = sqrt3 or x = -sqrt3 or x = 12 or x = 1`

Hence, all the zeroes are `sqrt3, -sqrt3`, 12 and 1.