Home » » If $$\alpha, \beta$$ are the roots of equation 18 + 15x - 3x2 = 0, find $${\alpha}\beta - {\alpha}-\beta$$...

# If $$\alpha, \beta$$ are the roots of equation 18 + 15x - 3x2 = 0, find $${\alpha}\beta - {\alpha}-\beta$$...

### Question

If $$\alpha, \beta$$ are the roots of equation 18 + 15x - 3x2 = 0, find $${\alpha}\beta - {\alpha}-\beta$$

A) 11

B) -11

C) 10

D) -10

### Explanation:

$$18 + 15x - 3x^2 = 0$$
$$a = - 3, b = 15, c = 18$$
$$\alpha +\beta =\frac{-b}{a}=\frac{-15}{-3}=5$$
$$\mathit{\alpha \beta }=\frac c a=\frac{18}{-3}=-6$$
$$\mathit{\alpha \beta }-\alpha -\beta =\mathit{\alpha \beta }-\left(\alpha +\beta \right)$$
$$= -6 - (5) = - 11$$

## Dicussion (1)

• $$18 + 15x - 3x^2 = 0$$
$$a = - 3, b = 15, c = 18$$
$$\alpha +\beta =\frac{-b}{a}=\frac{-15}{-3}=5$$
$$\mathit{\alpha \beta }=\frac c a=\frac{18}{-3}=-6$$
$$\mathit{\alpha \beta }-\alpha -\beta =\mathit{\alpha \beta }-\left(\alpha +\beta \right)$$
$$= -6 - (5) = - 11$$