If alpha and beta are the zeroes of the polynomial P(x)=4x²+3x+7, then find the value of alpha²+beta².
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Hey dear !!!
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==> In the given equation ,
p(x) = 4x² + 3x + 7
And α = alpha , β = beta are the zeroes of the given polynomial .
We have to find the value of ,
1/α + 1/β
So, lets find this,
We have the following values ,as
a = 4,b = 3,c = 7
We know that,
α + β = -b/a
= -3/4
Also we know that,
αβ = c/a
= 7/4
Now, by using the identity of quadratic expression ,[ 1/α + 1/β = α+β/αβ ]
By putting the obtained value we get,
1/α + 1/β = α+β/αβ
= -3/4/74
4 and 4 get cancelled and we get
= -3/7
Therefore 1/α + 1/β = -3/7
Thanks !!!
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