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