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If two zeroes of the polynomial x^4-6x^3...

If two zeroes of the polynomial `x^4-6x^3-26 x^2+138 x-35`are `2+-sqrt(3)`, find other zeroes.

Text Solution

Verified by Experts

Given that, two zeroes of polynomial. thus, they are the factors of the given poynomial.
Thus, `(x-2-sqrt3)xx(x-2+sqrt3)` is also a factor.
`:. x^2-4x+1` is a factor of polynomial.
Now, divide the polynomial to find out other factor.
Now, find zeroes of `x^2-2x-35`
The factors are, `(x+5)(x-7)=0`
thus, `x=-5 or 7` are zeros.
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