Question

please guys I really need your help with this one. Given that P(x)=ax² +bx +1, P(1) =6, and P(-1)=2, determine the values of a and b. polynomials​

Answer 1

P(x)=ax² +bx +1

____________________________

p (1) = a(1)²+b(1)+1 =6

=a+b+1=6

=a+b=6-1

=a+b=5_______(1)

____________________________

p(-1)=a(-1)²+b(-1)+1=2

=a(1)-b+1=2

=a-b+1=2

=a-b=2-1

=a-b=1_______(2)

____________________________

Solving both the equations;

a + b = 5

a - b = 1 +

2a = 6

a=3

Substituting a =3 in (1)

3-b=1

-b=-2

b=2

The value of a=3 & b=2

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Answer 2

Answer:

P(x)=ax² +bx +1

____________________________

p (1) = a(1)²+b(1)+1 =6

=a+b+1=6

=a+b=6-1

=a+b=5_______(1)

____________________________

p(-1)=a(-1)²+b(-1)+1=2

=a(1)-b+1=2

=a-b+1=2

=a-b=2-1

=a-b=1_______(2)

____________________________

Solving both the equations;

a + b = 5

a - b = 1 +

2a = 6

a=3

Substituting a =3 in (1)

3-b=1

-b=-2

b=2

The value of a=3 & b=2