Question

If Alpha, Beta are the
roots of the equation
3x²+7x-2=0 Find the
values of
alpha/beta + beta/alpha​

Answer 1

alpha/beta+beta/alpha

(alpha²+beta²)/alpha*beta

alpha+beta=-b/a=-7/3

alpha*beta=c/a=-2/3

alpha²+beta²=(alpha+beta)² - 2*alpha*beta

alpha²+beta²=49/9-(-4/3)

alpha²+beta²=49/9+4/3

alpha²+beta²=61/9

therefore,

your answer is

61/9÷-2/3

61/9*-3/2

-122/3

Answer 2

Answer:

37/6

Step-by-step explanation:

3x² + 7x - 2 = 0

$\alpha + \beta = \:( - b \div a) = (- 7 \div 3) \\ \alpha \beta = (c \div a) = ( - 2\div 3)\\ ( \alpha \div \beta ) \: + \: ( \beta \div \alpha ) \\ = \: ( { \alpha }^{2} + { \beta }^{2} ) \div ( \alpha \beta ) \\ = \: ({( \alpha + \beta )}^{2} - (2 \alpha \beta )) \div ( \alpha \beta ) \\ = \: ({( \alpha + \beta )}^{2} \: \div ( \alpha \beta )) - ((2 \alpha \beta ) \div ( \alpha \beta )) \\ = \: ({( \alpha + \beta )}^{2} \: \div ( \alpha \beta )) - (2) \\ = \: ({( - 7 \div 3)}^{2} \div ( - 2 \div 3)) - (2) \\ = \: (49 \div 6) - 2 \\ = \: 37 \div 6$