Question

If f(x)=3x³+ax²+5x−1 and f(2)=1, what is the value of a?

Answer 1

Answer: a = -8

Step-by-step explanation: Substition

f(2) means that we plug in 2 for x inside the function.

f(2) = 3*(2)^3 + a*2^2 +5*2 -1

f(2) = 24 + 4a + 9 = 33 + 4a

We also know f(2) = 1:

So 33+4a=1, a=-8

Answer 2

The value of a in the polynomial equation f(x)=3x³+ax²+5x−1 when f(2)=1 is found by substituting x with 2 in the equation and solving for a. It simplifies to 4a = 1 - 24 - 9, resulting in a = -8.

Step-by-step explanation:

To find the value of a in the polynomial equation f(x)=3x³+ax²+5x−1 given that f(2)=1, we must substitute x with 2 and set the equation equal to 1:

f(2) = 3(2)³ + a(2)² + 5(2) − 1 = 1

This simplifies to:

f(2) = 3(8) + a(4) + 10 − 1 = 24 + 4a + 9 = 1

Moving the constants to the right side and solving for a:

4a = 1 - 24 - 9

4a = -32

a = −8

Therefore, the value of a is −8.