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 p, q, r in R and r gt p gt 0 . If the quadratic equation px^(2) + qx + r = 0 has two complex roots alpha and beta , then |alpha|+|beta| , is

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

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

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

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 a ne 0 and the equation ax ^(2)+bx+c=0 has two roots alpha and beta such thet alpha lt -3 and beta gt 2. Which of the following is always true ?

If a, b, c ∈ R, a ≠ 0 and the quadratic equation ax^2 + bx + c = 0 has no real root, then show that (a + b + c) c > 0

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

Statement-1: If a ne 0 and the equation ax^(2) + bx + c = 0 has two roots alpha and beta such that alpha lt -1 and beta gt 1 , then a+|b|+c and a have the opposite sign. Statement-2: If ax^(2) + bx + c , is same as that of 'a' for all real values of x except for those values of x lying between the roots.

The quadratic equation x^(2)-9x+3=0 has roots alpha and beta.If x^(2)-bx-c=0 has roots alpha^(2)and beta^(2), then (b,c) is