"Question 4 Find the zero of the polynomial in each of the following cases: (i) p(x) = x + 5 (ii) p(x) = x − 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x − 2 (v) p(x) = 3x (vi) p(x) = ax, a ≠ 0 (vii) p(x) = cx + d, c ≠ 0, c, are real numbers.
Class 9 - Math - Polynomials Page 35"
Answers
x+5=0
x=-5
2) p(x)=x-5
x-5=0
x=5
3)p(x)=2x+5
2x+5=0
2x=-5
x=-5/2
Zero of a polynomial p(X) is a number a ,such that p(a)=0.
Zero of a polynomial is also called the root of polynomial.
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Put the given polynomial equal to zero to get an equation . Then solve, this equation and find the value of x, This value of x will give the zero of given polynomial.
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Solution:
(i)
p(x)=x+5
On Putting p(x)= 0
⇒x+5=0
⇒x=−5
Hence,x=-5 is a zero of the polynomial p(x).
(ii)
p(x)=x−5
On Putting p(x)= 0
⇒x−5=0
⇒x=5
Hence, x= 5 is a zero of the polynomial p(x).
(iii) p(x)=2x+5
On Putting p(x)= 0
⇒2x+5=0
⇒2x=−5
⇒x=−5/2
Hence, x=−5/2 is a zero of the polynomial p(x).
(iv)
p(x)=3x–2
On Putting p(x)= 0
⇒3x−2=0
⇒3x=2
⇒x=2/3
Hence, x= 2/3 is a zero of the polynomial p(x).
(v)
p(x)=3x
On Putting p(x)= 0
⇒3x=0
⇒x=0
Hence, x= 0 is a zero of the polynomial p(x).
vi)
p(x)= ax, a≠0
On Putting p(x)= 0
⇒ax=0
⇒x= 0/a= 0
⇒x= 0
Hence, x= 0 is the zero of the polynomial p(x).
vii)
p(x)= cx+d
On Putting p(x)= 0
cx+d= 0
cx= -d
x= -d/c
Hence, x= -d/c is the zero of the polynomial p(x).
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