Question

if alpha, beta are roots find the value of 1/alpha^2+1/beta^2​

Answer 1

Answer:

hello

Step-by-step explanation:

a*sqrt(x) + b*x + c = 0 be a quadratic equation

Now,Let

alpha , beta be the roots of the quadratic equation (Since only 2 roots can exist for a quadratic equation)

We know that,

sum of roots=alpha + beta = -b/a=> eqn (1)

product of roots=alpha*beta=c/a=>eqn (2)

(a+b)^2=a^2+b^2+2*a*b

Now consider,

alpha^2+beta^2=[(alpha+beta)^2] - [2*alpha*beta]

= [(-b/a)^2] - [2c/a]

=b^2/a^2 - 2c/a

=(b^2-2ac)/a^2

Hence for the given quadratic equation,

alpha^2+beta^2 =(b^2-2ac)/a^2