Find all the zeros of the polynomial P(x) if two of its zeros are √2 and -√2.Given that P(x) is STEP BY STEP EXPLAINATION
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Find all the zeros of the polynomial P(x) if two of its zeros are √2 and -√2.Given that P(x) is STEP BY STEP EXPLAINATION
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Polynomial :-
To find :-
According to the question,
(x + √2) & (x - √2) are the factors of polynomial 2x⁴ - 3x³ - 3x² + 6x - 2.
➞ (x + √2) (x - √2) = x² - 2
Now, we have to divide (2x⁴ - 3x³ - 3x² + 6x - 2) by (x² - 2).
So, the quotient is 2x² - 3x + 1.
Now, we have to factories it by using middle term factor.
➞ 2x² - 3x + 1
➞ 2x² - 2x - x + 1
➞ 2x(x - 1) - 1(x - 1)
➞ (2x - 1) (x - 1)
Now,
➝ 2x - 1 = 0
➝ x = ½
➝ x - 1 = 0
➝ x = 1