If alpha, beta are the zeros of the polynomial p(x)= x2 + 1, then find value of
Alpha +beta/(alpha x beta)^2
Answers
Answered by
1
Answer:
alpha+beta = -b/a
where b is the coefficient of X here X is not present so coefficient is 0,
then alpha+ beta =0
then alpha+beta/(alpha×beta)^2 is also 0
Answered by
2
Step-by-step explanation:
Given :-
α and β are the zeros of the polynomial
P(x)= x²+ 1.
To find :-
Find value of ( α+β )/(αβ)² ?
Solution :-
Given Quadratic Polynomial is P(x) = x²+1
On comparing with the standard quadratic polynomial ax²+bx+c
a = 1
b = 0
Since there is no term with the coefficient of x
c = 1
Given zeroes are α and β
We know that
Sum of the zeores = α+β = -b/a
=> α+β = -0/1
=> α+β = 0 --------------(1)
Product of the zeroes = αβ= c/a
=> αβ = 1/1
=> αβ = 1 ----------------(2)
Now the value of ( α+β )/(αβ)²
=> 0/1²
=> 0/1
=> 0
Therefore, ( α+β )/(αβ)² = 0
Answer:-
The value of ( α+β )/(αβ)² for the given problem is 0
Used formulae:-
- The standard quadratic polynomial is ax²+bx+c
- Sum of the zeores = α+β = -b/a
- Product of the zeroes = αβ= c/a
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