Consider the equation ` x ^(3) -ax ^(2) +bx-c=0,` where a,b,c are rational number, `a ne 1.` it is given that ` x _(1), x _(2) and x _(1)x_(2)` are the real roots of the equation. Then `x _(1) x _(2) ((a +1)/(b +c))=`

If euation x^(3) + ax^(2) + bx + c = 0, where a, b, c in Q (a ne 1). If the real roots of the equation are x_(1), x_(2) and x_(1)x_(2), then prove that x_(1)x_(2) is rational.

The roots of a_(1)x^(2)+b_(1)x+c_(1)=0 are reciprocal of the roots of the equation a_(2)x^(2)+b_(2)x+c_(2)=0 if

If a,b are the roots of the equation x^(2)+x+1=0, thn a^(2)+b^(2)= a.1b.2c-1d.3

If (x-1)^(2) is a factor of ax^(3) +bx^(2) +c then roots of the equation cx^(3) +bx +a=0 may be

Let a, b, c be non-zero real roots of the equation x^(3)+ax^(2)+bx+c=0 . Then

The number of roots of the equation,x-(2)/(x-1)=1-(2)/(x-1) is 0(b)1(c)2(d)3

If a and b are roots of the equation x^2+a x+b=0 , then a+b= (a) 1 (b) 2 (c) -2 (d) -1

Let x_(1),x_(2) are the roots of the quadratic equation x^(2) + ax + b=0 , where a,b, are complex numbers and y_(1), y_(2) are the roots of the quadratic equation y^(2) + |a|yy+ |b| = 0 . If |x_(1)| = |x_(2)|=1 , then prove that |y_(1)| = |y_(2)| =1