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.

If 1,2,3 are the roots of the equation x^(3) + ax^(2) + bx + c=0 , then

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

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

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

Number of roots of the equation 2sqrt(2x+1)=2x-1 is 0 (b) 1 (c) 2 (d) 3

Number of roots of the equation 2sqrt(2x+1)=2x-1 is 0 (b) 1 (c) 2 (d) 3

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

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