» » » Given that $$\alpha$$ and $$\beta$$ are the roots of the equation $$3x^2 - 5x - 7 = 0$$, find the roots of $$\alpha^2 + \beta^2 - \alpha \beta$$....

# Given that $$\alpha$$ and $$\beta$$ are the roots of the equation $$3x^2 - 5x - 7 = 0$$, find the roots of $$\alpha^2 + \beta^2 - \alpha \beta$$....

### Question

Given that $$\alpha$$ and $$\beta$$ are the roots of the equation $$3x^2 - 5x - 7 = 0$$, find the roots of $$\alpha^2 + \beta^2 - \alpha \beta$$.

### Options

A)
$$-\frac{36}{9}$$
B)
$$\frac{4}{9}$$
C)
$$\frac{46}{9}$$
D)
$$\frac{88}{9}$$

## Discussion (4)

• The answer to the question. Hope it's understood

• Anthony

3x$$a^{b}2$$ - 5x - 7 = 0
a = 3, b = -5, c = -7
$$\alpha^{2}+ \beta^{2} - \alpha\beta Since (\alpha + \beta)^{2} - 2\alpha\beta is the same as \alpha^{2} + \beta^{2} Then ( \alpha + \beta )^{2} - 2\alpha\beta - \alpha\beta ( \alpha + \beta )^{2} - 3\alpha\beta \alpha + \beta = \cfrac{-b}{a}, \cfrac{5}{3} \alpha\beta = \cfrac{c}{a}, \cfrac{-7}{3} \therefore (\cfrac{5}{3})^{2} - (3 \times -\cfrac{7}{3}) \cfrac{25}{9} + 7 \frac{25 + 63}{9} = \cfrac{88}{9}$$

1. Please can you solve it and snap it... I do not understand it like this