If `a` is the root (having the least absolute value) or the equation `x^2-b x-1=0(b in R^+)` , then prove that `-1

If the roots of the equation (b-c)x^(2)+(c-a)x+(a-b)=0 are equal,then prove that 2b=a+c

If roots of equation a-b)x^(2)+(b-c)x+(c-a)=0 are equal then prove that b+c=2a

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

Least value of the sum of the squares of the roots of the equation x^(2)-(a-2)x-a-1=0 is

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

If (1)/(sqrt(alpha)) and (1)/(sqrt(beta)) are the roots of equation ax^(2)+bx+1=0(a!=0,(a,b in R)), then the equation x(x+b^(3))+(a^(3)-3abx)=0 has roots -

If the sum of the squares of the roots of the equation x^(2) - (a-2) x - (a + 1) = 0 is least, then the value of a, is