Question

The 4/3x^2+4x+1 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is abc? Give your answer in simplest form.

Answer 1

Answer:

-4

Step-by-step explanation:

4/3x^2+4x+1= 4/3(x^2+3x+9/4)-3+1

                   = 4/3(x+3/2)^2 - 2

hence abc=4/3*3/2*(-2)

Answer 2

Given : The 4/3x^2+4x+1 can be written in the form a(x+b)^2+c, where a, b, and c are constants.

To find : The value of abc

solution : 4/3 x² + 4x + 1 = a(x + b)² + c

⇒4/3(x² + 3x) + 1 = a(x + b)² + c

⇒4/3[x² + 2.(3/2)x + (3/2)² - (3/2)²] + 1 = a(x + b)² + c

⇒4/3[(x + 3/2)² - 9/4] + 1 = a(x + b)² + c

⇒4/3(x + 3/2)² - 4/3 × 9/4 + 1 = a(x + b)² + c

⇒4/3(x + 3/2)² - 3 + 1 = a(x + b)² + c

⇒4/3(x + 3/2)² + (-2) = a(x + b)² + c

on comparing we get,

a = 4/3 , b = 3/2 and c = -2

so, the value of abc = 4/3 × 3/2 × -2 = -4

Therefore the value of abc is -4.