Obtain all the zeroes of the polynomial f(x)= 2x⁴-2x³-7x²+3x+6, if its two zeroes are√3/2 and - √3/2

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Obtain all the zeroes of the polynomial f(x)=
2x4-2x3-7x2+3x+6, if its two
zeroes are√3/2 and - √3/2

Aakash Sharma · Accepted Answer

Given: f(x) = 2x4 â€“2x3 â€“ 7x2 + 3x + 6 $and \sqrt{\frac{3}{2}} and - \sqrt{\frac{3}{2}} are the zeroes of f (x) \Rightarrow (\sqrt{2} x - \sqrt{3}) and (\sqrt{2} x + \sqrt{3}) are the factors of f (x) \Rightarrow (\sqrt{2} x - \sqrt{3}) (\sqrt{2} x + \sqrt{3}) = 2 x^{2} - 3 is the factor of f (x)$ Now

So, f (x) = 2x4 â€“ 2x3 â€“ 7x2 + 3x + 6 = (2x2 â€“ 3) (x2 â€“ x â€“ 2) = (2x3 â€“ 3) (x + 1) (x â€“ 2) Hence the other two zeroes of f (x ) are â€“ 1 and 2

Obtain all the zeroes of the polynomial f(x)= 2x4-2x3-7x2+3x+6, if its two zeroes are√3/2 and - √3/2

Obtain all the zeroes of the polynomial f(x)= 2x⁴-2x³-7x²+3x+6, if its two zeroes are√3/2 and - √3/2