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.

Prove that the equation x^(2)(a^(2)b^(2))+2x(ac+bd)+(c^(2)+d^(2))=0 has no real root if adnebc .

Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx+c=0, beta is the zero of a^2x^2-bx-c=0 and 0 , alpha < beta then prove that the equation a^2x^2+2bx+2c=0 has a root gamma that always satisfies alpha < gamma < beta.

If a ,b ,c are non zero rational no then prove roots of equation (a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 are rational.

If the equation (b^2 + c^2) x^2 -2 (a+b) cx + (c^2 + a^2) = 0 has equal roots, then

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

If A ,Ba n dC are the vetices of a triangle A B C , then prove sine rule a/(sinA)=b/(sinB)=c/(sinC)dot

If tanthetaa n dsectheta are the roots of a x^2+b x+c=0, then prove that a^4=b^2(b^2-4ac)dot

If roots of equation x^2+2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If a, b, c are the sides of a triangle ABC such that x^2+2(a+b+c)x+3lambda(a b+b c+c a)=0 has real roots.then