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vodka [1.7K]
2 years ago
7

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

Mathematics
1 answer:
galina1969 [7]2 years ago
4 0

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}}

<u>Hence</u><u> the</u><u> </u><u>value</u><u> of</u><u> </u><u>A </u><u>is </u><u>-</u><u>7</u><u>/</u><u>2</u><u>.</u>

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