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

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

If a,b,c epsilon R and abgt0, a+2b+4c=0 then equation ax^2+bx+c=0 has (A) both roots positive (B) both roots negative (C) one positive and one negative root (D) both roots imginary

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:

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

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 a, b and c are positive real and a = 2b + 3c , then the equation ax^(2) + bx + c = 0 has real roots for

If positive numbers a,b,c are in H.P.then equation x^(2)-kx+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

If b>a, then the equation (x-a)(x-b)-1=0 has (a) both roots in (a,b)( b) both roots in (-oo,a)(c) both roots in (b,+oo)( d)one root in (-oo,a) and the other in (b,+oo)