Question

Alpha,beta are the roots of of quadratic equation 9xsquare-10x+11=0.find the value of alpha square+beta square​

Answer 1

Answer:

11,-1

Step-by-step explanation:

Equation -> $x^2-10x+11=0$

Roots -> α , β

Sum of roots ->  α + β = $-b/a$

α + β = 10 [ $-b/a=-(-10)/9$ ]                     $--------> eq 1$

Product of roots -> α x β = $c/a$

α x β = $11/9$  [$c/a=11/9$]                            

$\alpha = 11/9\beta$                                                     $--------> eq 2$

putting value of α from eq 2 in eq 1

$11/9\beta + \beta = 10$

$11 + 9\beta ^2 = 90\beta$

$9\beta ^2 - 90\beta +11 =0$

on solving the equation

β = 11,-1