If alpha and beta are the two zeroes of the polynomial x2+5x+6, then find the value of 1/alpha+1/beta
Answers
Answer:
- 5 / 6
Step-by-step explanation:
Given :
α, β are the zeroes of polynomial x² + 5x + 6
Comparing x² + 5x + 6 with ax² + bx + c we get,
- a = 1
- b = 5
- c = 6
Sum of zeroes = α + β = - b / a = - 5 / 1 = - 5
Product of zeroes = αβ = c / a = 6 / 1 = 6
Now 1 / α + 1 / β
= ( β + α ) / αβ
= ( α + β ) / αβ
= - 5 / 6
Therefore the value of 1 / α + 1 / β is - 5/6.
Answer:
-5/6
Note:
★ The possible values of the variable for which the polynomial becomes zero are called its zeros.
★ A quadratic polynomial can have atmost two zeros.
★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;
• Sum of zeros , (α + ß) = -b/a
• Product of zeros , (αß) = c/a
Solution:
Here,
The given quadratic polynomial is ;
x² + 5x + 6 .
Clearly ,
a = 1
b = 5
c = 6
Now,
=> Sum of zeros = -b/a
=> α + ß = -5/1 = -5 ---------(1)
Also,
=> Product of zeros = c/a
=> αß = 6/1 = 6 -----------(2)
Now,
1/α + 1/ß = (ß + α)/αß
= (α + ß)/αß
= -5/6
Hence,
The required value of 1/α + 1/ß is (-5/6) .