Question

# Given that $$x - \sqrt 5$$ is a factor of polynomial $${x^3} - 3\sqrt 5 {x^2} - 5x + 15\sqrt 5$$, find all zeroes of the polynomial.

Solution

## Divisor $$x-\sqrt5$$Polynomial $$x^3-3\sqrt5 x^2 -5x+15\sqrt5$$Quotient$$=x^2-2\sqrt{5}x-15$$To find other zeroes , we will use common factor theorem$$x^2-3\sqrt5+\sqrt5 x-15$$$$x(x-3\sqrt5)+\sqrt5(x-3\sqrt5)$$$$(x+\sqrt5)(x-3\sqrt5)$$To find zeroes , equals the factors to zero.other zeroes $$=-\sqrt5 ,3\sqrt5$$Maths

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