Question

Directions:

Answer the questions below.
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Solve each quadratic equation. Write your answer as a simplified fraction when applicable. Always write the lesser number first.

(1 point)
Quadratic Equation Your Answer
1 (x+3)(x−1)=0
x =
and x =
2 (15x−5)(7+x)=0
x =
and x =
3 (13x−2)(x−34)=0
x =
and x =
4 30=x2+13x
x =
and x =


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Answer 1

Let's solve each of the quadratic equations:

### 1. (x + 3)(x - 1) = 0
To find the roots, set each factor to zero:
- \( x + 3 = 0 \) → \( x = -3 \)
- \( x - 1 = 0 \) → \( x = 1 \)

So, the answers are:
- x = -3 and x = 1

### 2. (15x - 5)(7 + x) = 0
Set each factor to zero:
- \( 15x - 5 = 0 \) → \( 15x = 5 \) → \( x = \frac{5}{15} = \frac{1}{3} \)
- \( 7 + x = 0 \) → \( x = -7 \)

So, the answers are:
- x = -7 and x = \( \frac{1}{3} \)

### 3. (13x - 2)(x - 34) = 0
Set each factor to zero:
- \( 13x - 2 = 0 \) → \( 13x = 2 \) → \( x = \frac{2}{13} \)
- \( x - 34 = 0 \) → \( x = 34 \)

So, the answers are:
- x = \( \frac{2}{13} \) and x = 34

### 4. 30 = x² + 13x
Rearrange this into standard form:
- \( x² + 13x - 30 = 0 \)

Now, factor:
We need two numbers that multiply to -30 and add to 13. The numbers are 15 and -2.
So we can write:
- \( (x + 15)(x - 2) = 0 \)

Set each factor to zero:
- \( x + 15 = 0 \) → \( x = -15 \)
- \( x - 2 = 0 \) → \( x = 2 \)

So, the answers are:
- x = -15 and x = 2

### Summary of Answers
1. x = -3 and x = 1
2. x = -7 and x = \( \frac{1}{3} \)
3. x = \( \frac{2}{13} \) and x = 34
4. x = -15 and x = 2

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