If `ax^2 + bx + c = 0, a, b, c in R` has no real zeros, and if a + b + c + `lt` 0, then

If ax^(2) + bx + c = 0 , a , b, c in R has no real roots, and if c lt 0, the which of the following is ture ? (a) a lt 0 (b) a + b + c gt 0 (c) a +b +c lt 0

If ax^(2)+bx+c=0 , a ne 0 , a , b , c in R has distinct real roots in (1,2) , then a and 5a+2b+c have

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

Consider a quadratic equation ax^2 + bx + c = 0 having roots alpha, beta . If 4a + 2b + c > 0,a-b+c 0 then |[alpha] + [beta]| can be {where [] is greatest integer}

If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha 2 , then

If ax^2+bx+c=0 and cx^2 + bx+a=0(a,b,c in R) have a common non-real roots, then which of the following is not true ?

If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, then a. c(a-b+c)>0 b. c(a+b+c)>0 c. c(4a-2b+c)>0 d. none of these

ax^2 + bx + c = 0(a > 0), has two roots alpha and beta such alpha 2, then

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbeta,w h e r ealpha >1 , then show that 1+c/a+|b/a|<0