Question

if alpha and beta are zeroes of polynomial p(x)=2x2-7x+5. Find a polynomial whose zeroes are 2alpha+1 and 2beta+3

Answer 1

Given :- 2x² - 7x + 5

Now ,

by middle term splitting we factorise it !!

2x² - 7x + 5

2x² - 5x - 2x + 5

x ( 2x - 5 ) - 1 ( 2x - 5 )

( x - 1 ) ( 2x - 5 )

___________________


*( x - 1 ) = 0

x = 1

*( 2x - 5 ) = 0

x = 5/2



Now,

let alpha = 1 nd beta = 5/2


For second polynomial :-

first zero is :- 2alpha + 1

2 × 1 + 1

= 2 + 1

= 3


second zero :- 2beta + 3

2 × 5/2 + 3

= 5 + 3

= 8


Now , to form a polynomial we have a formula that is :-

=> x² - ( sum of zeros ) x + ( product of zeros )

So, for forming new polynomial
we have to find sum and product of zeros


* Sum of zeros :-

3 + 8 = 11


* Product of zeros :-

3 × 8 = 24


so, by the formula

we get,

x² - 11x + 24

So, our required polynomial is x² - 11x + 24

@Altaf

Answer 2

Answer: Here is your answer

Step-by-step explanation:

Given :- 2x² - 7x + 5

Now,

by middle term splitting, we factorize it !!

2x² - 7x + 5

2x² - 5x - 2x + 5

x ( 2x - 5 ) - 1 ( 2x - 5 )

( x - 1 ) ( 2x - 5 )

___________________

*( x - 1 ) = 0

x = 1

*( 2x - 5 ) = 0

x = 5/2

Now,

let alpha = 1 nd beta = 5/2

For the second polynomial:-

first zero is :- 2alpha + 1

2 × 1 + 1

= 2 + 1

= 3

second zero :- 2beta + 3

2 × 5/2 + 3

= 5 + 3

= 8

Now, to form a polynomial we have a formula that is:-

=> x² - ( sum of zeros ) x + ( product of zeros )

So, for forming a new polynomial

we have to find the sum and product of zeros

* Sum of zeros:-

3 + 8 = 11

* Product of zeros:-

3 × 8 = 24

so, by the formula

we get,

x² - 11x + 24

So, our required polynomial is x² - 11x + 24

Thanks