Question

if alpha and beta are zeros of quadratic polynomial X square + 2 X + 1 find the value of one by Alpha Plus One by beta

Answer 1

Proper Question : If α and ß are Zeroes of Quadratic Polynomial x² + 2x +1 . Find the Value of 1/α + 1/ß


Solution :

In this Question, It is Given that α and ß are Zeroes of Quadratic Polynomial x² + 2x +1 .


Quadratic Polynomial = x² + 2x + 1

Here, a= 1 , b = 2 and C = 1



•°• Sum of Zeroes = -b/a ✒ -(Coefficient of x)/Coefficient of x²

°•° Sum of Zeroes = -(2)/1 ✒ -2


Also, Product of Zeroes = c/a ✒ Constant term Coefficient of x²

•°• Product of Zeroes = 1/1 ✒ 1


Now, From the Quadratic Polynomial!

Let the Polynomial be f(x)


•°• f(x) = x² + 2x + 1


Sum of Zeroes of Polynomial and Product of Zeroes of Polynomial are (-2) and (1) Respectively!


✏ Value of 1/α + 1/ß

✏ α+ß/ab

✏ -2 / 1

✏ -2


[ Therefore, Required Value of the 1/α + 1/ß is (-2) ]

Answer 2

Given that : α and β are Zeroes of Quadratic Polynomial x² + 2x +1 .



Let the Quadratic Polynomial be f(x)

f(x)= x² + 2x +1 .


Sum of Zeroes = -b/a => -(Coefficient of x)/Coefficient of x²

Sum of Zeroes = -(2)/1 -2


Product of Zeroes = c/a => Constant term Coefficient of x²

Product of Zeroes = 1/1






= Value of 1/α + 1/ β

= α+. β/aβ

= -2 /1

= -2


Hence, Required Value of the 1/α + 1/ß is (-2)