Question

quadratic eqn 2x-3y=16 and x-5y=22​

Answer 1

If you mean x = alpha and y = beta then..

x - 5y = 22 ......(eq.ii)

2x - 3y = 16 ......(eq.i)

x = 16+3y/2

putting value of x in eq. (ii)

(16+3y)/2 - 5y = 22

(16+3y-10y)/2 = 22

-7y = -14

y = 14/7 = 2

x = (16+3y)/2

x = (16+6)/2

x = 22/2 = 11

Required equation = (x - alpha)(x - beta)

0 = (x - 2)(x - 11)

0 = x² - 11x - 2x + 22

0 = x² - 13x + 22