Answer:
[tex]\dfrac{-7}{2}[/tex]
Step-by-step explanation:
Here we are given a polynomial ,
[tex]\implies f(x) = 2x^3 + Ax^2 + 4x - 5 [/tex]
And the value of ,
[tex]\implies f(2) = 5 \dots (i) [/tex]
And we need to find out the value of A . Firstly substitute x = 2 in f(x) , we have ,
[tex]\implies f(2) = 2(2)^3+ A(2)^2 + 4(2) -5 [/tex]
Simplify the exponents ,
[tex]\implies f(2) = 2(8) + A(4) + 8 - 5 [/tex]
Simplify by multiplying ,
[tex]\implies f(2) = 16 + 4A + 3 [/tex]
Add the constants ,
[tex]\implies f(2) = 19 + 4A [/tex]
Now from equation (i) , we have ,
[tex]\implies 19 + 4A = 5 [/tex]
Subtracting 19 both sides,
[tex]\implies 4A = 5-19 [/tex]
Simplify,
[tex]\implies 4A = -14[/tex]
Divide both sides by 4 ,
[tex]\implies A =\dfrac{-14}{4}=\boxed{ \dfrac{-7}{2}}[/tex]
Hence the value of A is -7/2.
