Question

If a quadratic equation with one unknown x^2 + x +c =0 have real root, what is the range of c?

Answer 1

we have x² + x + c = 0 compare the given equation with ax² + bx + c = 0 we have,

a = 1, b = 1 and c = 0

we know that quadratic equation of the form ax² + bx + c = 0 has real roots if and only if,

we have b = 1, a = 1 and c = c hence x² + x + c = 0 has real roots if and only if,

we can write,

Hence we can say that quadratic equation with one unknown x^2 + x + c =0 have real root than c ranges from c = -infinity to c = 0.25

or we can write c lies between - < c 0.25

in interval notation we can write range of c is given by,

or we can also write,