If `ax^(2)+bx+c = 0` has no real roots and a, b, c `in` R such that `a + c gt 0`, then

ax^(2)+2bx-3c=0 has no real root and a+b>3(c)/(4) then

Given that ax^(2)+bx+c=0 has no real roots and a+b+c 0 d.c=0

If a, b, c are real if ax^(2)+ bx + c = 0 has two real roots alpha, beta where a lt -1, beta gt 1 then

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

Let a,b,c in R and a gt 0 . If the quadratic equation ax^(2) +bx +c=0 has two real roots alpha and beta such that alpha gt -1 and beta gt 1 , then show that 1 + |b/a| + c/a gt 0

Let a,b,c in R and a gt 0 . If the quadratic equation ax^(2) +bx +c=0 has two real roots alpha and beta such that alpha gt -1 and beta gt 1 , then show that 1 + |b/a| + c/a gt 0

If the equation ax^(2) + 2 bx - 3c = 0 has no real roots and (3c)/(4) lt a + b , then

If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c in R,then