Question

if alpha and beta are the zeroes of the polynomial x²-5x+6 then find a quadratic polynomial whose zeroes are 2aplha+2 and 2beta+2 .​

Answer 1

Answer:

x^2-14x +48

Step-by-step explanation:

First we'll simplify the equation yo get the value of alpha and beta .

p(x)=0 = x^2-5x+6

x^2-3x-2x+6=0

x(x+-3)-2(x-3)=0

(x-2)(x-3)=0

x-2=0,x-3=0

alpha = x=2,beta=x=3

now zeroes of second polynomial

=2×2+2

=6

and

2×3+2=8

the required polynomial=

k(x^2-(alpha+beta)x +alpha×beta)

=k(x^2-(6+8)x +6×8)

when k=1,

x^2-14x+48