If `a ,b in R ,a!=0` and the quadratic equation `a x^2-b x+1=0` has imaginary roots, then `(a+b+1)` is a. positive b. negative c. zero d. Dependent on the sign of `b`

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.

The quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has equal roots if

If b gt a , then the equation (x-a)(x-b)-1=0 , has

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 has (a) at least one root in [0, 1] (b) at least one root in [1,2] (c) at least one root in [3/2, 2] (d) none of these

If the quadratic equation a x^2+b x+6=0 does not have real roots and b in R^+ , then prove that a > m a x{(b^2)/(24),b-6}

If a ,b ,c in Ra n da b c<0 , then equation b c x^2+2(b+c-a)x+a=0h a s (a)both positive roots (b)both negative roots (c)real roots (d)one positive and one negative root

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

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 a ,b ,c be the sides of A B C and equations a x^2+b x+c=0a n d5x^2+12x+13=0 have a common root, then find /_Cdot