Let `a , ba n dc` be the three sides of a triangle, then prove that the equation `b^2x^2+(b^2=c^2-alpha^2)x+c^2=0` has imaginary roots.

Let a,b and c be the three sides of a triangle. Suppose a and b are the roots of the equation x^(2)-(c+4)x+4(c+2)=0 and the largest angle of the triangle is

If 0 lt a lt b lt c and the roots alpha, beta of the equation ax ^(2)+bx+c=0 are imaginary, then

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

If the quadratic equation alpha x^(2)+beta x+a^(2)+b^(2)+c^(2)-ab-bc-ca=0 has imaginary roots then

Let a,b,c be the lengths of three sides of a triangle satistying the condition (a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0 .If the set of all possible values of x is the interval (alpha,beta) ,then 12(alpha^(2)+beta^(2)) is equal to:

If 0

If the roots of the equation x^(2)+2cx+ab=0 are real unequal,prove that the equation x^(2)-2(a+b)x+a^(2)+b^(2)+2c^(2)=0 has no real roots.

Let a<=b<=c be the lengths of the sides of a triangle.If a^(2)+b^(2)