If three zeroes of a polynomial x4 +3x3-4x2-12x are 2 , 0 , -2 , then find the fourth zero.
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Step-by-step explanation:
x
4
+3x
3
−20x
2
−6x+36
Two zeroes are
2
,−
2
∴(x−
2
)(x+
2
) are the factors of the polynomial
⇒x
2
−2 is a factor
∴ Quotient =x
2
+3x−18
To find other two factors
x
2
+3x−18=0⇒x
2
+6x−3x−18
⇒x(x+6)−3(x−6)
⇒(x+3)(x+6)=0
⇒x=3&−6
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