If the equation `|x^2+b x+c|=k` has four real roots, then
A. `b^2-4cgt0 and 0ltklt(4c-b^2)/ 4`
B. `b^2-4clt0 and 0ltklt(4c-b^2)/4`
C.`b^2-4cgt0 and kgt(4c-b^2)/4`
D. none of these

If the roots of x^2-bx +c=0 are two consecutive integers then b^2-4c=

If the roots of the equation x^(2)-bx+c=0 are two consecutive integers, then b^(2)-4c is

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

If the roots of ax^(2)+bx+c=0 are real and equal then ………….. A) b^(2)-4ac lt 0 B) b^(2)-4ac=0 C) b^(2)-4ac gt 0 D)cannot say

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

If the both roots of the equation x^(2)-bx+c=0 be two consecutive integers, then b^(2)-4c equals

If alpha,beta are the roots of the equation a x^2+b x+c=0, then the value of aalpha^2+c//aalpha+b+(abeta^2+c)//(abeta+b) is (b(b^2-2a c))/(4a) b. (b^2-4a c)/(2a) c. (b(b^2-2a c))/(a^2c) d. none of these

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, then a. 3a >2+4c b. 3a<2+4c c. c < a d. none of these

If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e c^2theta as its roots, then which of the following must hold good? (a.) b+c=0 (b.) b^2-4a cgeq0 (c.) c ccgeq4a (d.) 4a+bgeq0