The roots of the equations `x ^2−x−3=0 ` are a. imaginary b. rational. c. irrational d. none of these.

If a+b+c=0, a,b,c in Q then roots of the equation (b+c-a) x ^(2) + (c+a-c) =0 are: Rational Irrational Imaginary none of these .

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, then

Prove that both the roots of the equation x^(2)-x-3=0 are irrational.

The equation ax^(2)+6x-9=0 will have imaginary roots if

If rational numbers a,b,c be th pth, qth, rth terms respectively of an A.P. then roots of the equation a(q-r)x^2+b(r-p)x+c(p-q)=0 are necessarily (A) imaginary (B) rational (C) irrational (D) real and equal

If a and c are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a) real and distinct (b) real and equal (c) imaginary (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 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.