Question

How are roots of any quadratic equation denoted by?
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Answer 1

Answer:

How are the roots of a quadratic equation related to its coefficients?

The standard form of quadratic equation is ax^2 +bx + c =0, where a, b,c are constants with a not equal to 0.

Here a and b are called the coefficients, and c is called the constant term.

The roots of the quadratic equation are given by alpha = {-b + rt (b^2–4ac)}/2a} and beta = {-b - rt (b^2–4ac)}/2a}

When we add the roots we have alpha + beta = -2b/2a = -b/a.

When we multiply the roots we have alpha . beta ={(-b)^2 - (b^2–4ac)} /4a^2 = 4ac/4a^2 = c/a

Hence we have sum of the roots =-b/a and product of the roots = c/a in a quadratic equation.