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maths
chapter name : polynomial
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Answer:
a) Here, p(x)=3x.
In order to find zero of p(x), we equate p(x) to 0,
i.e p(x)=0.
⇒3x=0⇒x=0.
∴ 0 is the zero of p(x).
b) x
2
+5x+6=0
x
2
+2x+3x+6=0
x(x+2)+3(x+3)=0
(x+2)(x+3)=0
x=−2,−3
c) p(x)=(x+2)(x+3) This is a quadratic polynomial . It has two zeroes .
Let P(x)=0
⇒(x+2)(x+3)=0
⇒x+2=0,x+3=0
⇒x=−2,x=−3
∴ The zeroes of the polynomial are
−2 and −3.
d) P(x)=x
4
−16
Let ,
P(x)=0
⇒x
4
−16=0
⇒(x
2
)
2
−4
2
=0
⇒(x
2
−4)(x
2
+4)=0
⇒(x+2)(x−2)(x
2
+4)=0
⇒x+2=0,x−2=0,x
2
+4=0
⇒x=−2,x=2,x=±
−4
∴ The zeroes of the polynomial are
−2,2 and ±
−4
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