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# Find the equation whose roots are $$2$$ and $$-3\frac{1}{2}$$

### Question

Find the equation whose roots are $$2$$ and $$-3\frac{1}{2}$$

### Options

A) 2x2 + 3x + 14 = 0

B) 2x2 + 5x + 7 = 0

C) 2x2 + 5x - 7 = 0

D) 2x2 + 3x - 14 = 0

### Explanation:

$$x^2 - (\text{sum of roots})x + \text{product of roots} = 0$$
$$x^2 - (2 + (-3\frac{1}{2}))x + (2)(-3\frac{1}{2}) = 0$$
$$x^2 - (2 + (-\frac{7}{2}))x + (2)(-\frac{7}{2}) = 0$$
$$x^2 - (2 - \frac{7}{2})x + (-7) = 0$$
$$2x^2 + 5x - 7 = 0$$

## Discussion (2)

• $$x^2 - (\text{sum of roots})x + \text{product of roots} = 0$$
$$x^2 - (2 + (-3\frac{1}{2}))x + (2)(-3\frac{1}{2}) = 0$$
$$x^2 - (2 + (-\frac{7}{2}))x + (2)(-\frac{7}{2}) = 0$$
$$x^2 - (2 - \frac{7}{2})x + (-7) = 0$$
$$2x^2 + 5x - 7 = 0$$