Question

c) 3.2x² = 3x + 11
0 = 11, b = 3, c = 3.2
11 + 3x + 3.2x² - 3.2x² = 0

Explanation:

Step1: Rearrange the equation

Start with the given equation \( 3.2x^2 = 3x + 11 \). Subtract \( 3x \) and \( 11 \) from both sides to get it in standard quadratic form \( ax^2 + bx + c = 0 \).
\( 3.2x^2 - 3x - 11 = 0 \)

Step2: Identify coefficients

For a quadratic equation \( ax^2 + bx + c = 0 \), here:

• \( a = 3.2 \) (coefficient of \( x^2 \))
• \( b = -3 \) (coefficient of \( x \))
• \( c = -11 \) (constant term)

Wait, maybe there was a miscalculation earlier. Let's re - check the original rearrangement. If we start from \( 3.2x^2=3x + 11 \), moving all terms to the left: \( 3.2x^2-3x - 11 = 0 \). But in the hand - written work, it seems there was a different approach. Let's go back to the first step of the hand - written solution. The original equation is \( 3.2x^2=3x + 11 \), then when we do \( 11 + 3x+3.2x^2-3.2x^2 = 0 \)? Wait, no, let's do it properly.
Let's start over. The equation is \( 3.2x^{2}=3x + 11 \).
Subtract \( 3x \) and \( 11 \) from both sides:
\( 3.2x^{2}-3x - 11=0 \)
Now, if we compare with \( ax^{2}+bx + c = 0 \), we have \( a = 3.2 \), \( b=-3 \), \( c = - 11 \). But in the hand - written work, it seems like there was a mistake in the sign of \( b \) or \( c \). However, if we follow the hand - written step where \( 11 + 3x+3.2x^{2}-3.2x^{2}=0 \), that simplifies to \( 11 + 3x=0 \), which is wrong. So the correct way is to rearrange \( 3.2x^{2}-3x - 11 = 0 \).
But maybe the original equation was written incorrectly. Let's assume that the equation is \( 3.2x^{2}=3x + 11 \), and we want to write it in standard quadratic form \( ax^{2}+bx + c = 0 \).

Step1: Move all terms to left

Subtract \( 3x \) and \( 11 \) from both sides:
\( 3.2x^{2}-3x - 11 = 0 \)
So \( a = 3.2 \), \( b=-3 \), \( c=-11 \). But in the hand - written work, it says \( a = 11 \), \( b = 3 \), \( c = 3.2 \), which is incorrect. So the correct coefficients are \( a = 3.2 \), \( b=-3 \), \( c=-11 \).

Answer:

If we consider the standard quadratic form \( ax^{2}+bx + c = 0 \) for the equation \( 3.2x^{2}-3x - 11 = 0 \), then \( a = 3.2 \), \( b=-3 \), \( c=-11 \). If we follow the incorrect hand - written step, but the correct mathematical approach gives us \( a = 3.2 \), \( b=-3 \), \( c=-11 \).