Question

)
Find the equation of polynomial whose zeros are v3 and -13:
(a) x2-9
(b) x2-3
(c) XP-6
(d) x + 3​

Answer 1

Answer:

As x→0 lim

(2+ x 37(x) )

exist so f(x) should be ax 5 +bx 4 +cx 3

∴ x→0 lim

(2+ x 3ax 5+bx 4 +cx 3 )=4

2+c=4⇒c=2

f ′ (x)=5ax 4 +4bx 3 +6x 2

As at x=I

1 f has critical point

∴f (1)=0⇒5a+4b+b=0 ___(I)

f ′ (−1)=0⇒5a−4b+b=0 ___(II)

From equation (I) & (II)

b=0

a=−6/5

∴f(x)= 5−6 x 5 +2x 3

f (x)=−6x 4 +6x 2

=6x 2 (−x 2 −1)

=−6x 2 (x−1)(x+1)