The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. what is the function’s input value?

function’s input value is x = 2, 7/2.

Step-by-step explanation:

Given :  f(x) = 2x² + 3x + 5  when evaluated, gives a value of 19.

To find : What is the function’s input value.

Solution : We have given that  f(x) = 2x² + 3x + 5

2x² + 3x + 5 = 19

On subtracting  on side by 19

2x² + 3x + 5 -19 = 0

2x² + 3x - 14 = 0

On factoring

2x² - 4x + 7x -14 = 0

Taking common 2x from first two terms and 7 from last two terms

2x( x - 2 ) + 7 ( x - 2 ) = 0

On grouping

( 2x + 7)  ( x -2) = 0

x - 2 = 0

x = 2 ,

2x + 7 =0

x = -7/2 .

Let check for both values 2(2)² + 3(2) + 5 = 8 +6 +5 = 19.

2(7/2)² + 3(-7/2) + 5 = 24.5 - 10.5 + 5 = 19

Therefore, function’s input value is x = 2, 7/2.

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