Q) Find all the zeroes of the polynomial x^4 - 3x^3 + 6x - 4, if two of it's zeroes are root 2 and root -2.

Thank you.

Question

Q) Find all the zeroes of the polynomial x^4 - 3x^3 + 6x - 4, if
two of it's zeroes are root 2 and root -2

Thank you

Saksham Tolani · Accepted Answer

Dear student,

Let p(x)=x4-3x3+6x-4since 2 and -2 are the zeroes of p(x) (Assuming)then x+2 and x-2  are the factors of p(x)∴x+2× x-2 =x2-2      --[using a2-b2=(a+b)(a-b)]Now, divide p(x) by x2-2 we get                     x2-3x+2       x2-2 x4 -3x3+0x2+6x-4                   x4         -4x2               -                 +                           -3x3+2x2+6x                              -3x3        +6x                            +               -                                             2x2         -4                                        2x2         -4                                      -          +                                              0      Now, we factorize   x2-3x+2=0⇒ x2-2x-x+2=0⇒xx-2-1x-2=0⇒x-1x-2=0⇒x=1 and x=2 are the zeroes of p(x) therefore, the zeroes of p(x) are 2, -2 , 1, 2
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Q) Find all the zeroes of the polynomial x^4 - 3x^3 + 6x - 4, if two of it's zeroes are root 2 and root -2. Thank you.

Q) Find all the zeroes of the polynomial x^4 - 3x^3 + 6x - 4, if two of it's zeroes are root 2 and root -2.

Thank you.