Question

if alpha and beta are zeros of x square minus 4x +3 . find a quadratic polynomial whose zeroes are 1/3alpha+beta and 1/3beta+alpha.

Answer 1

Answer:

3x²-26x+20

Step-by-step explanation:

given alpha,beta are the roots of x²-4x+3

then alpha=1,beta=3

1/3 alpha+ beta,1/3beta+alpha

1/3(1)+3,1/3(3)+1

10/3,2 are the roots of

k(x²-(alpha+beta)x+(alpha.beta))

k(x²-(10/3+2)x+(10/3.2)

k((3x²-26x+20)/3)

let k=3

the 3x²-26x+3 is the required quadratic polynomial