Let `a >0,b >0` and `c >0` . Then, both the roots of the equation `a x^2+b x+c=0` are a. real and negative b.have negative real parts c. have positive real parts d. None of the above

If a, b are real then show that the roots of the equation (a-b)x^(2)-6(a+b)x-9(a-b)=0 are real and unequal.

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 aa n dc 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

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

If a

If l ,m ,n are real l!=m , then the roots of the equation (l-m)x^2-5(l_+m)x-2(l-m)=0 are a. real and equal b. Complex c. real and unequal d. none of these

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

The equation 4ax^2 + 3bx + 2c = 0 where a, b, c are real and a+b+c = 0 has

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these