if a and b are zeroes of the polynomial p(x)=4x²+3x+7,then 1/a+1/b is equal to
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Given,
Polynomial p(x) = 4x^2+3x+7
a and b are the zeroes of the polynomial.
The coefficient of x^2 = 4
The coefficient of x = 3
and constant term = 7
We know that,
alpha + beta = -b/a = coefficient of x/coefficient of x^2
so, a + b = -3/4
and alpha × beta = c/a = constant term/coefficient of x^2
a×b = 7/4
By using the identity:
1/alpha+1/beta = alpha + beta/alpha×beta
so now, 1/a+1/b = a+b/ab
substitute the values of ab and a+b.
-3/4÷7/4
-3/4×4/7
-3/7
Therefore the value of 1/a+1/b = -3/7.
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