Question

Obtain all the zeroes of the polynomial X^4 - 3√2 x³ + 3x² +3 √2x - 4 = 0 , if two of it's zeroes are √2 and 2√2 ... Guys , Solve out without using constant A in the easiestethod​

Answer 1

Answer:

P(x) = x⁴ - 3 √2 x³ + 3 x² + 3√2 x - 4

given that (x - √2) , (x - 2√2) are factors of P(x) as √2 and 2√2 are two zeroes of P(x) = 0.

(x -√2) (x - 2√2) = x² -3√2 x + 4 is a factor of P(x). let A be a constant. We can write the constant term in the second factor by : -4/4 = -1... dividing the constant terms.

let (x² - 3√2 x + 4) (x² + A x -1 ) = P(x)

Now compare the coefficients of x³ : A - 3√2 = -3√2 => A = 0

coefficient of x : 4A + 3√2 = 3√2 => A = 0

so the other factors are : x² - 1 = 0

so x = 1 and -1 are the other factors.

This method of multiplying the factors and comparing coefficients is simple

thank you!!!