Question

Can anyone help me how to do this que.

Answer 1

Zeroes are root2 and - root2

=> ( x + root2) and ( x - root2) are factor of given polynomial.

We know that product of two factors of given number is also the factor of given number.

So,

=> ( x^2 - 2) is factor of given polynomial

Now,

On dividing the given polynomial by ( x^2 - 2)

Quotient = ( x^2 + 3x - 18)

Since the Divisor is factor of given polynomial,

The quotient will also be the factor of given polynomial.

Now,

On factorising the quotient,

x^2 + 3x - 18

= x^2 + 6x - 3x - 18

= x ( x +6) - 3(x +6)

= ( x + 6) (x - 3)

Other zeroes are 3 and - 6