Question

plz give me answer ........ . ........

Answer 1

Heya !!!

Let Alpha = 2/3


And,


Beta = -1/4


Sum of zeroes = Alpha + Beta = 2/3 - 1/4 = ( 8 - 3 ) /12 = 5/12


And,


Product of zeroes = 2/3 × -1/4 = -2/12 = -1/6


Therefore,


Required quadratic polynomial = X²-(Sum of zeroes )X + Product of zeroes.



=> X² - (5/12)X + (-1/6)



=> X² - 5X/12 - 1/6


=> 12X² - 5X - 2 / 12 = 0


=> 12X² - 5X - 2




Here,


A= Coefficient to X² = 12


B = Coefficient to X = -5

And,



C= Constant term = -2


Relationship between the zeroes and Coefficient.




Sum of zeroes = -B/A



Alpha + Beta = -(B/A )



ALPHA + BETA = 5/12


AND,


product of zeroes = C/A



Alpha × Beta = -2/12 = -1/6



★ HOPE IT WILL HELP YOU ★

Answer 2

$\alpha = \frac{2}{3} \\ \beta = \frac{ - 1}{4} \\ equation \: is \: {x}^{2} + (\alpha + \beta )x + (\alpha \beta ) \\ {x}^{2} + ( \frac{2}{3} - \frac{1}{4} ) + ( \frac{2}{3} \times \frac{1}{4} ) \\ {x}^{2} + \frac{5}{12} x - \frac{2}{12} = 0 \\ 12 {x}^{2} + 5x - 2 = 0$
$\alpha + \beta = - \frac{b}{a}$
b=5
a=12
c=-2
$\alpha + \beta = \frac{5}{12} \\ \frac{ - b}{a} = \frac{ - ( - 5)}{12} \\ hence \: \: \: \: \: \alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{ - 2}{12} \\ \frac{c}{a} = \frac{2}{12} \\ hence \: we \: can \: say \: that \alpha \beta = \frac{c}{a}$