if aplha,beta are the zeros of the polynomial p(x) = x^2+x+1,then 1/alpha + 1/beta is
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if aplha,beta are the zeros of the polynomial p(x) = x^2+x+1,then 1/alpha + 1/beta is
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[tex]\large \bf \clubs \: Given :- [/tex]
p(x) = x² + x + 1.
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[tex]\large \bf \clubs \: To \: Find :- [/tex]
Value of [tex] \sf\dfrac{1}{\alpha}+\dfrac{1}{\beta}[/tex]
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[tex]\large \bf \clubs \: Main \: Formula :- [/tex]
☆ Relationship between Zeros and coefficiants of a Quadratic Polynomial :
For a qudratic polynomial of the Form ax² + bx + c
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[tex]\large \bf \clubs \: Solution :- [/tex]
We Have ,
α and β are the zeros polymomial
p(x) = x² + x + 1.
Hence ,
[tex]\large \pmb{ \alpha + \beta = - 1 } \: \: \:----(1) \: \\ \\ \large\pmb{ \alpha \beta = 1} \: \: \:---- (2)[/tex]
Now,
[tex]\large \dfrac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ \large \sf = \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ \bf \: \: \: \: \{using \: (1) \: and \: (2) \} \\ \\ \large\sf = \frac{ - 1}{1} \\ \\ = -1 \\ \\ \purple{ \Large :\longmapsto \underline { \pmb{\boxed{{ \frac{1}{ \alpha } + \frac{1}{ \beta } = - 1 } }}}}[/tex]
[tex] \Large\red{\mathfrak{ \text{W}hich \:\:is\:\: the\:\: required} }\\ \LARGE \red{\mathfrak{ \text{ A}nswer.}}[/tex]
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Answer:
Given :
Solution
x² + x + 1
Here :-
Sum of zeroes : α + β = (-b/a)
Product of zeroes : α x β = c/a
To find :
Answer :
Answer = (-1)
Hope it helps you :)