Question

alpha/3beta+beta/3alpha=​?
write in the form of alpha+beta and alpha beta

Answer 1

Answer:

4x^2-5x+2.let the zeroes be alpha and beta.

sum of zeroes(alpha+beta)=-b/a=-(-5)/4=5/4

product of zeroes(alpha×beta)=c/a=2/4=1/2

let the zeroes of f(x) be 3alpha+betaand 3 beta+alpha

sum of zeroes=3alpha+beta+alpha+3beta

=4alpha+4beta

=4(alpha+beta)

=4×5/4=5

product of zeroes=(alpha+3beta)(3alpha+beta)

=3alpha^2+alpha×beta+9×alpha×beta+3beta^2

3alpha^2+10×alpha×beta+3beta^2

3(alpha^2+beta^2)+10×1/2

3(25/16-1)+5

3(9/16)+5

27/16+5

107/16

f(x)=x^2-(sum of zeroes)x+product of zeroes

=x^2-5x+107/16

=1/16(16x^2-80x+107)

Answer 2

Answer:

alpha+beta/ 3(alpha x beta)

Step-by-step explanation:

alpha/3beta+ beta/3alpha

= alpha + beta/3alpha x 3beta

= alpha + beta / 3(alpha x beta)