Question

5. Obtain all other zeroes of the polynomial x^4 - x^3 - 15x² + 3x + 36, if two of its
zeroes are √3 and -√3.
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Answer 1

Step-by-step explanation:

The answer is in the above image

Answer 2

we are given two zeroes :-

√3 and -√3

we have to find :-

other zeroes of p(x) x^4 - x^3 - 15x² + 3x + 36

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the given zeroes can be written as,

(x-√3) and (x+√3)

Now,

(x - √3)(x + √3)

= x^2 + √3x - √3x - 3

cancel +√3x and -√3x

= x^2 - 3

Therefore, x^2 - 3 is a factor of p(x).

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Now, we divide p(x) by x^2 - 3

( refer attachment for division )

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To find other zeroes of p(x), we factorise the quotient, or use the quadratic formula.

Quotient = x^2 - x - 12

On factorizing,

(x+3)(x-4)

x = -3 or, x = 4

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•°• other zeroes are -3 and 4