Question

Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x -2 if two of its zeroes are √2 and ‒√2.

Answer 1

Hey dear !!

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==> In The example we have,

p(x) = 2x⁴ - 3x³ - 3x² + 6x - 2

We have also given that √2 and -√2 are the two zeroes of the given polynomial.

∴ ( x + √2) ( x - √2)

=> x² - 2

Now, divide the given polynomial by x² -2 we will use long division method.

Refer from the attachment which I have provided .

Now, you can see in the photo that we got the value of Quotient as 2x² -3x +1

So, now we can easily find the other zeroes of this polynomial by using splitting the middle term .

=> 2x² - 3x + 1

=> 2x² - 2x - x + 1

=> 2x( x - 1) - 1( x - 1)

=> ( x -1) (2x - 1)

∴ ( x - 1 )= 0

∴ x = 1

and

∴ (2x -1) = 0

∴ 2x = 1

∴ x = 1/2

Therefore, the zeroes of the given polynomial are 1 , 1/2 , √2 and -√2 .

Thanks !!!

[ Be Brainly ]

Answer 2

Answer:

1 and 1/2

Step-by-step explanation:

(x-root2)(x+root2)

x2-2

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

=2x2-3x+1

(2x-1)(x-1)

x=1/2 x=1