To find $a$ and $b$ in the quadratic equation $x^2 + ax + b = 0$, we need to know the roots of the equation. Suppose the roots of the equation are $r_1$ and $r_2$. The quadratic equation can be expressed in terms of its roots as follows:

$(x - r_1)(x - r_2) = 0$

Expanding this, we get:

$x^2 - (r_1 + r_2)x + r_1r_2 = 0$

By comparing this with the standard form $x^2 + ax + b = 0$, we can identify the coefficients $a$ and $b$ as follows:

• $a = -(r_1 + r_2)$
• $b = r_1r_2$

So, given the roots $r_1$ and $r_2$, you can find $a$ and $b$ using these formulas.

Would you like an example to illustrate this?

---

Here are five questions you might ask next:

1. If the roots of $x^2 + ax + b = 0$ are 2 and 3, what are $a$ and $b$?
2. How do you find the roots of $x^2 + 4x + 4 = 0$?
3. What are the coefficients $a$ and $b$ if the roots are -1 and -5?
4. Can you derive the quadratic equation given roots 3 and -2?
5. How does the sum and product of roots relate to the coefficients in a quadratic equation?

Tip: The sum and product of the roots of a quadratic equation provide a straightforward way to determine the coefficients $a$ and $b$.