If both roots of the equation `a x^2+x+c-a=0` are imaginary and `c > -1,` then a.`3a >2+4c` b.`3a<2+4c` c.`c < a` d. none of these

If both roots of the equation a(x^2-1)+x+c are imaginary and c gt -1 then

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 the roots of the equation x^2-2a x+a^2-a-3=0 are real and less than 3, then (a) a<2 b. 2<-alt=3 c. 3 4

If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, then for all real values of x, the expression 3b^2x^2+""6b c x""+""2c^2 is (1) greater than 4ab (2) less than 4ab (3) greater than - 4a b (4) less than - 4a b

If the roots of the equation x^(2)-bx+c=0 are two consecutive integers, then b^(2)-4c is

If the roots of the equation a x^2-b x+c=0a r ealpha,beta, then the roots of the equation b^2 c x^2-a b^2x+a^3=0 are 1/(alpha^3+alphabeta),1/(beta^3+alphabeta) b. 1/(alpha^2+alphabeta),1/(beta^2+alphabeta) c. 1/(alpha^4+alphabeta),1/(beta^4+alphabeta) d. none of these

If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt(1-a^2)=0 are a. real b. imaginary c. both equal d. none of these

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)

If the roots of the equation x^(2)+px+c=0 are 2,-2 and the roots of the equation x^(2)+bx+q=0 are -1,-2, then the roots of the equation x^(2)+bx+c=0 are

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot