f a ,b are the roots of the quadratic equation ,x²+x+1=0 then find the value of 1/a , 1/b.
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C O R R E C T Q U E S T I O N :
If α , β are the roots of the quadratic equation ,x²+x+1=0 then find the value of 1/α + 1/β .
S O L U T I O N :
Given :
- α , β are the roots of the quadratic equation.
- Quadratic equation, x² + x + 1 = 0.
To Find :
- The value of 1/α + 1/β.
Explanation :
Given, Quadratic equation, x² + x + 1 = 0.
On comparing with, ax² + bx + c = 0 , We get ;
⟶ a = 1 , b = 1 , c = 1
★ Sum of roots,
⟶ α + β = -b/a
⟶ α + β = -1/1
⟶ α + β = -1
★ Product of roots,
⟶ αβ = c/a
⟶ αβ = 1/1
⟶ αβ = 1
Now,
1/α + 1/β
⟶ α + β/αβ
⟶ -1/1
⟶ -1
Therefore,
The value of 1/α + 1/β is -1.
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