Question

if alpha and beta are the zeros of the polynomial 4x^2-x-4,find the quadratic polynomial whose zeros are 2-alpha and 2-beta​

Answer 1

Answer :  Hi friend !

Hi friend !

p(x) = 4x² - x - 4

a = 4 , b = -1 , c = -4

α and β are zeros of p(x)

we know that ,

sum of zeros = -b/a

that is ,

α + β = -b/a = 1/4

product of zeros = c/a

that is ,

αβ = -4/4 = -1

==========================

1/2α and 1/2β are zeros of a polynomial

sum of zeros = 1/2α + 1/2β

= 2α + 2β / 4αβ

= 2 [α + β] / 4αβ

= [2 × 1/4] / 4× - 1

= (1/2)/ -4

= -1/8

product of zeros =( 1/2α )( 1/2β)

= 1/4αβ

= 1/4×-1

= -1/4

a quadratic polynomial is given by ,

k {x² - [ sum of zeros ]x + [ product of zeros ]}

k{x² - [-1/8]x - 1/4}

k{x² + 1/8x - 1/4}

putting k = 8

8(x² + 1/8x - 1/4 )

8x² + x - 2 ----> is the required polynomial

or

the correct answer is 8x^2-x-2.

since alpha & beta are the roots of the given equation, find alpha+beta & alpha×beta from the equation. then, put these values in the equation whose roots are alpha/2 & beta/2.

and also check the attachment

Step-by-step explanation: stay bless stay safe stay happy stay healthy be your self and be good