1. Find the value of polynomial at 3x^2 + 5x + 7
a). x = 0
b). x = -1
c). x = 1
d). x = -2
e). x = 2
Sol. a). P(x) = 3x^2
+ 5x + 7
Put x = 0
P(0) = 3*0 + 5*0 + 7 = 7
b). P(x) = 3x^2 + 5x
+ 7
Put x = -1
P(-1) = 3*(-1)^2 + 5*(-1) + 7
= 3 – 5 + 7 = 5
c). P(x) = 3x^2 + 5x
+ 7
Put x = 1
P(1) = 3*(1)^2 + 5*(1) + 7
= 3 + 5 + 7 = 15
d). P(x) = 3x^2 + 5x
+ 7
Put x = -2
P(-2) = 3*(-2)^2 + 5*(-2) + 7
= 3*4 – 5*2 + 7 = 12 – 10 + 7 = 9
e). P(x) = 3x^2 + 5x
+ 7
Put x = 2
P(2) = 3*(2)^2 + 5*(2) + 7
= 3*4 + 5*2 + 7 = 12 + 10 + 7 = 29
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| maths-ncert-solution |
2. Find the value of polynomial at 5x^2 - 3x + 2
a). x = 0
b). x = -1
c). x = 1
d). x = -2
e). x = 2
Sol. a). P(x) = 5x^2
- 3x + 2
Put x = 0
P(0) = 5*0 - 3*0 + 2 = 2
b). P(x) = 5x^2 - 3x
+ 2
Put x = -1
P(-1) = 5*(-1)^2 - 3*(-1) + 2
= 5 + 3 + 2 = 10
c). P(x) = 5x^2 - 3x
+ 2
Put x = 1
P(1) = 5*(1)^2 - 3*(1) + 2
= 5 - 3 + 2 = 4
d). P(x) = 5x^2 - 3x
+ 2
Put x = -2
P(-2) = 5*(-2)^2 - 3*(-2) + 2
= 5*4 + 3*2 + 2 = 20 + 6 + 2 = 28
e). P(x) = 5x^2 - 3x
+ 2
Put x = 2
P(2) = 5*(2)^2 - 3*(2) + 2
= 5*4 - 3*2 + 2 = 20 - 6 + 2 = 16
3. Find P(0), P(1) and P(2) for each of the following
polynomial :-
a). P(x) = ( 2x – 3 ) ( 2x + 3 )
b). 3 x^3 + 7
c). 4 x^2 + 7 x + 9
d). y^3 + y^2 +y +7
e). 3 z + 7
Sol. a). P(x) = ( 2x – 3 ) ( 2x + 3 )
Put x = 0
P(0) = ( 2*0 – 3 ) ( 2*0 + 3 ) = -3*3 = -9
Put x = 1
P(1) = ( 2*1 – 3 ) ( 2*1 + 3 ) = -1*5 = -5
Put x = 2
P(2) = ( 2*2 – 3 ) ( 2*2 + 3 ) = 1*12 = 12
b). P(x) = 3 x^3 + 7
Put x = 0
P(0) = ( 3*0 + 7 ) = 0 + 7 = 7
Put x = 1
P(1) = ( 3*1^3 + 7 ) = 3 + 7 = 10
Put x = 2
P(2) = ( 3*2^3 + 7 ) = 24 + 7 = 31
c). P(x) = 4 x^2 + 7 x + 9
Put x = 0
P(0) = ( 4*0 + 7*0 + 9 ) = 9
Put x = 1
P(1) = ( 4*1 + 7*1 + 9 ) = 4 + 7 + 9 = 20
Put x = 2
P(2) = ( 4*2^2 + 7*2 + 9 ) = 16 + 14 + 9 = 39
d). P(x) = y^3 + y^2 +y +7
Put y = 0
P(0) = ( 0^3 + 0*2 + 0 + 7 ) = 7
Put y = 1
P(1) = ( 1^3 + 1*2 + 1 + 7 ) = 1 + 1 + 1 + 7 = 10
Put y = 2
P(2) = ( 2^3 + 2*2 + 2 + 7 ) = 8 + 4 + 2 + 7 = 21
e). P(x) = 3 z + 7
Put z = 0
P(0) = ( 3*0 + 7 ) = 0 + 7 = 7
Put z = 1
P(1) = ( 3*1 + 7 ) = 3 + 7 = 10
Put z = 2
P(2) = ( 3*2 + 7 ) = 9 + 7 = 16
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