Question

if√5 and -√5 are the two zeros of the polynomial x^3+3x^2-5x-15, find it's 3rd zero
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Answer 1

Step-by-step explanation:

If √5 and -√5 are the zeroes of the given polynomial then,

x-√5 and x + √5 are the factors of x^3 + 3x^2 - 5x - 15

(x - √5)*(x + √5) = x^2 - 5( By using the property

( By using the property (a - b)(a + b) = a^2 + b^2

therefore, x^2 - 5 is a of factor of x^3 + 3x^2 - 5x - 15

on dividing x^3 + 3x^2 - 5x - 15 by x^2 - 5 we get

x + 3(For division see the attachment)

therefore, all factors of the given polynomial are :

x + √5, x - √5, x + 3

therefore all zeroes of the polynomial are:

x = -√5, √5, -3

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