Question

Find all the zeroes of the polynomial x 3 +3x ​2 -2x-6 if two of its zeroes -root 2 and root 2

Answer 1

If two zeroes are √2 and -√2
so, the factor will be
(x-√2)(x+√2) =0
⇒x²-2=0

now, dividing the expression with this,

x²-2)x³+3x²-2x-6( x+3
       x³       -2x
     -          +
          +3x²-6
          +3x²-6
          -      +
            0     0

so,x³+3x²-2x-6= (x²-2)(x+3)

Answer 2

Answer:

-3

Step-by-step explanation:

In x³ + 3x² -2x - 6,

a=1,  b=3

α =√2,  β= -√2

α + β + γ = -b/a

√2 - √2 + γ = -3/1

γ = -3