Question

if f(x) = 2x^3 + Ax^2 +4x -5 and f(2)=5, then what is the value of A?

Answer 1

Answer:

$\dfrac{-7}{2}$

Step-by-step explanation:

Here we are given a polynomial ,

$\implies f(x) = 2x^3 + Ax^2 + 4x - 5$

And the value of ,

$\implies f(2) = 5 \dots (i)$

And we need to find out the value of A . Firstly substitute x = 2 in f(x) , we have ,

$\implies f(2) = 2(2)^3+ A(2)^2 + 4(2) -5$

Simplify the exponents ,

$\implies f(2) = 2(8) + A(4) + 8 - 5$

Simplify by multiplying ,

$\implies f(2) = 16 + 4A + 3$

Add the constants ,

$\implies f(2) = 19 + 4A$

Now from equation (i) , we have ,

$\implies 19 + 4A = 5$

Subtracting 19 both sides,

$\implies 4A = 5-19$

Simplify,

$\implies 4A = -14$

Divide both sides by 4 ,

$\implies A =\dfrac{-14}{4}=\boxed{ \dfrac{-7}{2}}$

Hence the value of A is -7/2.