Question

85, Transform each of the following
equations into ones in which the
coefficients of the second highest power
of x is zero and also find their
transformed equations
(i) x3 -6x2 +10x-3=0.
(ii) x4 +4x3 + 2x2 - 4x-2=0


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Answer 1

Question

Transform each of the following

equations into ones in which the

coefficients of the second highest power

of x is zero and also find their

transformed equations

(i) x3 -6x2 +10x-3=0.

(ii) x4 +4x3 + 2x2 - 4x-2=0

Solution

[i]. (x3)-6x2+10x-3=0

x=-3

x=3-√13/2

=-0.303

x=3+√13/2

=3.303

[ii] x4 +4x3 + 2x2 - 4x-2=0

p(x)=x⁴+4x³+5x²+2x-2=0

if one of the roots id (-1+i) then (-1-i) is all as a root of p(x)

= { x-(-1+i)}{x(-1-i)} is a factor of p (x)

= (x+1)²-(i)² is a factor of p(x)

x²+2x+2 is a factor of p(x)

Dividing p(x) by x²+2x+2

p(x)=(x²+2x-1)(x²+2x+2)

(x²+2x-1) (x²+2x+2)

x²+2x-2=0

x=-2±√4-4(1)(-1)/2

x= -2±2√2/2

x= -1±√2

So,

[i] x3 -6x2 +10x-3=0.

=3.303

[ii] x4 +4x3 + 2x2 - 4x-2=0

x= -1±√2