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Question

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases :

(i) f(x) = 3x + 1, x = - 13

(ii) f(x) = x2 - 1, x = 1, -1

(iii) g(x) = 3x2 - 2, x = 23,23

(vi) p(x) = x3  6x2 + 11x - 6, x = 1,2,3

(v) f(x) = 5x -π,x=45

(vi) f(x) = x2,x = 0

(vii) f(x) = lx + m, = - ml

(viii) f(x) = 2x + 1, x = 12


Solution

(i) f(x) = 3x + 1, x = - 13

f(13)=3(13)+4

= - 1 + 1 = 0

x=13 is the zero of f(x) 

(ii) f(x) = x2 - 1, x=1, -1

f(1) =(1)2 - 1 = 1 -1 =0

x=1 is zero of f(x)

f(-1)=(1)2 - 1 = 1 = 0

x = - 1 is zero of f(x)

(iii) g(x) = 3x2 - 2, x = 23,23

g(23)=3(23)22=3×432

=4-2=2

x=23 is not its zero

g(23)=3(23)22

=3×432=42=2

x=23 is not its zero 

(iv) p(x) = x36x3 + 11x - 6, x = 1, 2,3

P(1) =(1)36(1)2 + 11(1) - 6

= 1 - 6 ×1+11× 1 - 6 = 1 - 6 + 11 - 6

=12 - 12 = 0

x = 1 is its zero

p(2) =(2)26(2)2+11× 2 - 6

= 8 - 6× 4 + 22 - 6 = 8 - 24 + 22 - 6

=30 - 30 = 0

x = 2 is its zero

P(3) =(3)36(3)2+11× 3 - 6

= 27 - 6× 9 + 33 - 6

= 27 - 54 + 33 - 6 = 60 - 60 = 0

x = 3 is its zero

Hence x = 1,2,3 are its zeros

(v) f(x) = 5x - π,x=45

=f(45)5×45π=4π

x=45 is not its zero

(vi) f(x) = x2,x = 0

f(0)=(0)2 = 0

x = 0 is its zero

(vii) f(x) = lx + m, x = - ml

f(ml)=1×(ml)+m

= - m + m = 0

=ml is its zero

(viii) f(x) = 2x + 1, x =12

f(12)=2×(12)2+1=2×14+1

=12+1=32

x=12 is not its zero


Mathematics
RD Sharma
Standard IX

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