Question

If α and β are the roots of quadratic equation 3x

2 − 5x − 2 = 0. Find α and β.​

Answer 1

Step-by-step explanation:

α,β are roots of 3x

2

−5x+2=0

α+β=−

a

b

=

3

5

a=3,b=−5,c=2

αβ=

a

c

=

3

2

β

α

+

α

β

=

αβ

α

2

+β

2

=

αβ

(α+β)

2

−2αβ

=

3

2

(

3

5

)

2

−2(

3

2

)

=

3

2

9

25

−

3

4

=

3

2

9

25−12

=

9

13

×

2

3

=

6

13

Answer 2

$3 {x}^{2} - 5x - 2 = 0 \\ 3 {x}^{2} - 6x + x - 2 = 0 \\ 3x(x - 2) + 1(x - 2) = 0 \\ (3x + 1)(x - 2) = 0 \\ 3x + 1 = 0 \: \: \: \: \: \: \: x - 2 = 0 \\ 3x = - 1 \: \: \: \: \: \: \: \: \: \: \: x = 2 \\ x = \frac{ - 1}{3} \: \: \: \: \: \: \: \: \: \: \: \:$

α = -1/3

β = 2