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Question

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Find the relation between the coefficient quadratic equations and the sum and the product of its solutions .Frame the general form of quadratic equation .when the solutions are given,

Answer 1

Generally, a quadratic equation looks like:

                    Ax^2 + Bx + C

A quadratic equation can also be written in the form of (x + a)(x + b),

where a and b are it's solutions.

When expanded, you would be able to find it in its general form of

x^2 + (a+b)x + ab.

Therefore the coefficients of the quadratic equation (assuming the value of A is 1), can be represented by the sum of the solutions (for the 'x' coefficient) and the product of the solutions (for the constant)

Ax^2 + BX + C = x^2 + (a+b)x + ab

assuming A = 1,  B = (a + b)

                          C = a * b