The given equation is:

$4x^2 = 2x - 3$

To express this in standard quadratic form $ax^2 + bx + c = 0$, we need to move all terms to one side of the equation:

$4x^2 - 2x + 3 = 0$

Now, we can identify the coefficients:

• $a = 4$ (coefficient of $x^2$)
• $b = -2$ (coefficient of $x$)
• $c = 3$ (constant term)

The question asks for the value of $b$, which is the coefficient of $x$. Therefore, the value of $b$ is:

$b = -2$

The correct answer is $-2$.

Would you like any further details or explanation?

Here are five related questions for further exploration:

1. How do you find the discriminant of a quadratic equation?
2. What are the roots of the quadratic equation $4x^2 - 2x - 3 = 0$?
3. What is the sum of the roots of this quadratic equation?
4. What is the significance of the $b^2 - 4ac$ term in quadratic equations?
5. Can a quadratic equation have complex roots, and how can we identify them?

Tip: Always remember to write quadratic equations in standard form before identifying coefficients.