If `s intheta,costheta` be the roots of `a x^2+b x+c=0` , then prove that `b^2=a^2+2ac. `

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

If x is real and the roots of the equation a x^2+b x+c=0 are imaginary, then prove tat a^2x^2+a b x+a c is always positive.

If x_1 and x_2 are the real and distinct roots of a x^2+b x+c=0, then prove that lim_(n->x_1){1+"sin"(a x^2+b x+c)}^(1/(x-x_1))=e^(a(x_1-x_2))

If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^2 are the roots of a^2x^2+b^2x+c^2=0 , then a ,b ,c are in (A) G.P. (B) H.P. (C) A.P. (D) none of these

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,beta+delta are the roots of A x^2+B x+C=0,(A!=0) for some constant delta then prove that (b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

If 8 and 2 are the roots of x^(2) + ax + c = 0 and 3,3 are the roots of x^(2) + dx + b = 0, then the roots of the equation x^(2) + ax + b = 0 are

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in R