The quadratic equation `ax^(2)+bx+c=0` has real roots if:

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 quadratic equation ax^(2)+bx+c=0 has real roots of opposite sign in the interval (-2,2), then prove that 1+(c)/(4a)-|(b)/(2a)|>0

The quadratic equation ax^(2)+5bx+2c=0 has equal, roots if

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

a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 has no real roots, then which one of the following is not true?

a, b, c, in R, a ne 0 and the quadratic equation ax^(2) + bx + c = 0 has no real roots, then which one of the following is not true?

If a,b,c are real distinct numbers such that a ^(3) +b ^(3) +c ^(3)= 3abc, then the quadratic equation ax ^(2) +bx +c =0 has (a) Real roots (b) At least one negative root (c) Both roots are negative (d) Non real roots

a, b, c in R, a!= 0 and the quadratic equation ax^2+bx+c=0 has no real roots, then

a, b, c in R, a!= 0 and the quadratic equation ax^2+bx+c=0 has no real roots, then