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# The graph is that of y = 2x2 - 5x - 3. For what value of x will y be negative? F...

### Question

The graph is that of y = 2x2 - 5x - 3. For what value of x will y be negative? For what value of x will y be negative?

### Options

A) -$$\frac{1}{2} \leq x$$ < 3

B) -$$\frac{1}{2} < x \leq 3$$

C) -$$\frac{1}{2} < x < 3$$

D) -$$\frac{1}{2} \leq x \leq 3$$

### Explanation:

2x2 - 5x - 3 = 0

2x2 - 6x + x - 3 = 0

2x(x - 3) + 1(x - 3) = 0

(2x + 1)(x - 3) = 0

2x + 1 = 0

2x = -1

x = -$$\frac{1}{2}$$

x - 3 = 0

-$$\frac{1}{2}$$ < x < 3

## Dicussion (1)

• 2x2 - 5x - 3 = 0

2x2 - 6x + x - 3 = 0

2x(x - 3) + 1(x - 3) = 0

(2x + 1)(x - 3) = 0

2x + 1 = 0

2x = -1

x = -$$\frac{1}{2}$$

x - 3 = 0

-$$\frac{1}{2}$$ < x < 3