Question

Find
the polynomial
equation whose
roots are the
reciprocals
of the
roots
of
x⁴-3x³+7x²+5x-2=0​

Answer 1

The given equation is x 2 −3x−4=0

x² −3x−4=0

⇒ x 2 −4x+x−4=0

⇒ x(x−4)+1(x−4)=0

⇒ (x−4)(x+1)=0

⇒ x=4 and x=−1

Taking reciprocal of roots we get,

⇒ x= 1/4 and x=−1

The required equation,

⇒ (x− 4/1) (x+1)=0

⇒ x² +x - x/4 - 1/4 =0

⇒ 4x²+4x−x−1=0 [ Multiplying both sides by

4 ]

∴ 4x² +3x−1=0