Question

if alpha and beta are the zeros of the quadratic polynomial X square + bx + c then evaluate ​

Answer 1

Answer:

bc/a³ ( 2b²-5ac )

Step-by-step explanation:

ax²+bx+c

αβ=c/a

α+β=-b/a

a( α²/β+β²/α) +b(α/β+β/α)

=a(α³+β³)/αβ + b(α²+β²)αβ

=a{ (α+β)(α²+β²-αβ) }/αβ + b { (α+β)²-2αβ } /αβ

=a { (α+β) { (α+β)²-3αβ }}/αβ +b { (α+β)²-2αβ }/αβ

putting the values of α+β and αβ

=a { (-b/a) { (-b/a)²-3c/a )} / (c/a) + b { (-b/a)²-2c/a } / (c/a)

=-b { b²/a²-3c/a } / (c/a) + b ( b²/a²-2c/a) /c/a

=(b /a²) ( b²-3ac ) /(c/a) +b/a² (b²-2ca) / (c/a)

=bc/a³( b²-3ac) +bc/a³ ( b²-2ca)

=bc/a³ ( b²-3ac +b²-2ac)

=bc/a³ ( 2b²-5ac )