Question

plz solve it fast.......​

Answer 1

Let,

P(x) = 2x⁴ - 3x³ - 3x² + 6x - 2

As given,

√2 and -√2 are factors of Polynomial.

(x+√2)(x-√2) is also a factor.

x² - 2 is also a factor.

Now, We shall divide Polynomial by its factor.

x²-2)2x⁴-3x³-3x²+6x-2( 2x²-3x+1

2x⁴ -4x²

-------------------------------------

-3x³ + x² +6x -2

-3x³ + 6x

---------------------------------------

x² - 2

x² - 2

----------------------------

0

Again,

2x² - 3x + 1 = 0

2x² - 2x - x + 1 = 0

2x(x-1) -1 (x-1) = 0

(2x - 1)(x-1) = 0

If,

2x - 1 = 0

x = 1/2

Or If,

x - 1 = 0

x = 1

Hence other two zeroes are 1/2 & 1.

Therefore, all the zeroes of Polynomial are √2 , -√2 , 1/2 and 1.