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Question

Question 3
Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x) = 3x + 1, x = 13
(ii) p(x)=5xπ,x=45
(iii) p(x)=x21,x=1,1
(iv) p(x) = (x +1) (x -2), x = - 1, 2
(v) p(x)=x2,x=0
(vi) p(x)=ix+m,x=mi
(vii) p(x)=3x21,x=13,23
(viii) p(x)=2x+1,x=12

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Solution

(i) Yes, 13 is the zero of the polynomial.
3x + 1 = 0, for x=13.

(ii) No, it is not the zero of the given pilynomial.
5xπ=5×45π=4π0

(iii) Yes, it is the zero of the polynomial.
x21=121=0 for x=1 and x21=(1)21=0 for x=1

(iv) Yes, it is the zero of the polynomial.
(x+1)(x2)=0 for x=1, or x=2

(v) Yes, it is the zero of the polynomial.
x2=0 for x=0

(vi) Yes, it is the zero of the polynomial.
Ix+m=0 for x=ml

(vii) 3x21=3131=0 for x=13and 3x21=3.431=30Thus, 13 is zero but 23 is not a zero of the polynomial. Ans.
(viii) No, it is not the zero of the polynomial.
2x+10 for x=12.

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