Question

find all zeros of the polynomial x4-3x3+6x-4 if two of its zeros are root 2 and -root 2.

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Answer 1

So the other two zeroes are 1 and

2

Refer the attached picture

Thank you

Answer 2

Solution :-

we know that, when a & b are the factors of given polynomial (x - a)(x - b) is exactly divide the given Polynomial.

So,

→ (x - √2)(x + √2)

→ (x² - 2) will Divide the polynomial x⁴ - 3x³ + 6x - 4..

x² - 2) x⁴ - 3x³ + 6x - 4 ( x² - 3x + 2

x⁴ - 2x²

-3x³ + 2x² + 6x

-3x³ + 6x

2x² - 4

2x² - 4

__0___

Quotient :- x² - 3x + 2

→ x² - 3x + 2 = 0

→ x² - 2x - x + 2 = 0

→ x(x - 2) - 1(x - 2) = 0

→ (x - 2)(x - 1) = 0

→ x = 2 & 1.

Hence, all zeros of the polynomial are { √2 , (-√2), 2 & 1}.