Question

What are the other zeros of a polynomial 2x⁴ - 3x³-3x² + 6x -2 ,if two of its zeros are √2 and -√2​

Answer 1

Answer:

1. Given roots are
2. $\sqrt{2}$and
3. $- \sqrt{2}$

for f(x)=2x⁴-3x³-3x²+6x-2

STEP BY STEP EXPLANATION:

1. Since root 2 is root of f(x)

=>x=

$\sqrt{2}$

=>x²–2=0

x²-2 is the factor of f(x)

2.Divide f(x) with x²-2

=> x²–2) 2x⁴-3x³-3x²+6x-2(2x²-3x+1

2x⁴+0x³-4x

- - +

__________________

–3x³+x²+6x

–3x²+0 +6x

+ - -

___________________

x²+0x–2

x²+0x–2

- - +

____________________

0

3.Now factorise 2x²-3x+1=0

=> 2x²–2x–x+1 =0

=> 2x(x–1)–1(x–1)=0

=> (x–1)(2x–1) =0

so x=1,x=1/2

By substituting above values of x in f(x),

we get

X=1

4.Similarly do the same process for x= –(sq root 2)

u will get another zero of f(x)