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The question asks to find the quadratic equation with roots \(-5\) and \(1\) using the sum and product of the roots formula.

Given:
- Roots: \( r_1 = -5 \) and \( r_2 = 1 \)

The sum of the roots \(S\) is:
\[
S = r_1 + r_2 = -5 + 1 = -4
\]

The product of the roots \(P\) is:
\[
P = r_1 \cdot r_2 = (-5) \cdot 1 = -5
\]

Using the standard form of a quadratic equation:
\[
x^2 - (S)x + P = 0
\]

Substituting the values of the sum and product:
\[
x^2 - (-4)x - 5 = 0
\]
\[
x^2 + 4x - 5 = 0
\]

So, the quadratic equation is:
\[
x^2 + 4x - 5 = 0
\]

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the relationship between the roots and the coefficients of a quadratic equation?
2. How would the equation change if the roots were both positive?
3. Can you derive the quadratic equation if the sum of the roots was given first?
4. What happens to the quadratic equation if the product of the roots is zero?
5. How do you factorize a quadratic equation to find its roots?

**Tip:** You can always verify a quadratic equation by plugging in the roots and checking if the equation holds true.

Tentukan persamaan kuadrat yang akar-akarnya -5 dan 1 dengan menggunakan rumus jumlah dan hasil kali akar-akar.

Learn how to find the quadratic equation when the roots are -5 and 1 using the sum and product of roots formula. This problem explains key algebraic concepts, including the quadratic equation and its roots, suitable for students in Grades 8-10.

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