Question

1. if 5/13 and -7 are roots to a quadratic equation, find the factors.

solutions:_________
factored form:____________________
quadratic form:____________________

Explanation:

Step1: Convert root to first factor

If $x=\frac{5}{13}$, rearrange to get $13x - 5 = 0$.

Step2: Convert root to second factor

If $x=-7$, rearrange to get $x + 7 = 0$.

Step3: Write factored form

Multiply the two factors: $(13x - 5)(x + 7)$

Step4: Expand to quadratic form

Use distributive property:

$$\begin{align*} (13x - 5)(x + 7)&=13x(x + 7) - 5(x + 7)\\ &=13x^2 + 91x - 5x - 35\\ &=13x^2 + 86x - 35 \end{align*}$$

Answer:

Solutions: $\frac{5}{13}, -7$
Factored Form: $(13x - 5)(x + 7)$
Quadratic Form: $13x^2 + 86x - 35$