If Alfa and beta are zeroes of the polynomial f(x)=x2+x-2,then find a polynomial whose zeroes are 2alfa+1 and 2beta+1
Answers
Answer:
x² - 9
Step-by-step explanation:
Given---> α and β are zeroes of the polynomial
( x² + x - 2 )
To find ---> A polynomial whose zeroes are
( 2α + 1 ) and ( 2β + 1 ) .
Solution--->ATQ,
α and β are zeroes of the polynomial ( x² + x - 2 ) .
We know that
Sum of zeroes
= - Coefficient of x/Coefficient of x²
=> Sum of zeroes = - 1 / 1
=> α + β = - 1
Product of zeroes
= Constant term / Coefficient of x²
=> α β = -2 / 1
=> α β = - 2
Now we have to find a polynomial whose zeroes are ( 2α + 1 ) and ( 2β + 1 )
Sum of zeroes = ( 2α + 1 ) + ( 2β + 1 )
= 2α + 2β + 1 + 1
= 2 ( α + β ) + 2
Putting α + β = -1 in it , we get,
= 2 ( - 1 ) + 2
= -2 + 2
Sum of zeroes = 0
Product of zeroes = ( 2α + 1 ) ( 2β + 1 )
= 4αβ + 2α + 2β + 1
Putting αβ = -2 and α + β = - 1 in it we get,
= 4 ( - 2 ) + 2 ( α + β ) + 1
= -8 + 2 ( - 1 ) + 1
= - 8 - 2 + 1
= - 10 + 1
= - 9
Now we know that requierd polynomial is,
x² - ( sum of zeroes )x + product of zeroes
= x² - ( 0 ) x + ( - 9 )
= x² - 9
#Answerwithquality
#BAL
Answer:
Step-by-step explanation:
To find ---> A polynomial whose zeroes are
( 2α + 1 ) and ( 2β + 1 ) .
Solution--->ATQ,
α and β are zeroes of the polynomial ( x² + x - 2 ) .
We know that
Sum of zeroes
= - Coefficient of x/Coefficient of x²
=> Sum of zeroes = - 1 / 1
=> α + β = - 1
Product of zeroes
= Constant term / Coefficient of x²
=> α β = -2 / 1
=> α β = - 2
Now we have to find a polynomial whose zeroes are ( 2α + 1 ) and ( 2β + 1 )
Sum of zeroes = ( 2α + 1 ) + ( 2β + 1 )
= 2α + 2β + 1 + 1
= 2 ( α + β ) + 2
Putting α + β = -1 in it , we get,
= 2 ( - 1 ) + 2
= -2 + 2
Sum of zeroes = 0
Product of zeroes = ( 2α + 1 ) ( 2β + 1 )
= 4αβ + 2α + 2β + 1
Putting αβ = -2 and α + β = - 1 in it we get,
= 4 ( - 2 ) + 2 ( α + β ) + 1
= -8 + 2 ( - 1 ) + 1
= - 8 - 2 + 1
= - 10 + 1
= - 9
Now we know that requierd polynomial is,
x² - ( sum of zeroes )x + product of zeroes
= x² - ( 0 ) x + ( - 9 )
= x² - 9