Question

$if \alpha + \beta = 20 \: and \: \alpha \beta = 40 \: find \: \alpha \: and \: \beta$
by full method

Answer 1

Heya Friend ☺
Alpha will be x and beta will be 20

because alpha +beta (sum of zeros)=-b/a
20/1

and product of zeros =c/a
40

Answer 2

I'm taking alpha as a and bita as b

given that

a+b= 20

a= 20-b. -------(1)

substitute a in another equation

( 20- b ) b =40

20b -b² = 40

b²-20b+40 =0

completing square method

b²-2× 10× b = -40

adding 10² on both sides

b²-2× 10× b+10²= -40 +10²

(b-10)²= -40+100

= 60

b-10 = √ 60

b= +√ 60+10 b= - √ 60+10

b= 7.7+10. b= -7.7+10

b= 17.7. b= 2.3

substitute b in 1

a= 20-2.3

a=17.7

and also other b

a= 20- 17.7

a = 2.3

CHECK

17.7 +2.3= 20

Hope it helps you......