Consider the quadratic equation ax^{2} + bx + c . Suppose that its roots are denoted α and β.

It is possible to show that

For example the equation given is 3x^{2 }-5x +c = 0 then α + β is 3/5 and α β is – 1

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Consider the quadratic equation ax^{3} + bx^{2} + cx + d . Suppose that its roots are denoted α , β and γ.

It is possible to show that

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If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots. Eg: x^{3}+5x^{2}+3x+9=0 has no positive roots as all the co-efficients of any powers of x are positive numbers

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For a bi-quadratic equation ax^{4}+bx^{3}+cx^{2}+dx+e = 0 , Suppose that its roots are denoted α , β, γ and Φ.

It is possible to show that

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