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`

If a,b,c in R and the quadratic equation x^(2)+(a+b)x+c=0 has no real roots then

If quadratic equation ax^(2)+bx+c=0 does not have real roots,then which of the following may be false (a) a(a-b+c)>0 (b) c(a-b+c)>0 e) b(a-b+c)>0 (d) a+b+c)(a-b+c)>0

Which of the following is not zero? (a) 0\ x\ 0 (b) 0/2 (c) ((6-6))/2 (d) 4+0

If the equation a x^2+b x+c=0(a >0) has two real roots alphaa n dbeta such that alphalt-2 and betagt2, then which of the following statements is/are true? (a)a-|b|+c<0 (b)clt0,b^2-4a cgt0 (c) 4a-2|b|+c<0 (d) 9a-3|b|+c<0

In the quadratic equation 4x^(2) - 2 ( a + c - 1) x + ac - b = 0 (a gt b gt c)

If the quadratic equations ax^(2)+bx+c=0(a,b,c epsilon R, a !=0) and x^(2)+4x+5=0 have a common root, then a,b,c must satisfy the relations

If the quadratic equation ax^(2)+2cx+b=0 and ax^(2)+2bx+c=0(b!=c) have a common root,then a+4b+4c=