Vieta's formulas

x_1+x_2=-\tfrac{b}{a},\quad x_1x_2=\tfrac{c}{a}

Result unit: — (liczba)

What it describes

Vieta's formulas relate the sum and product of the roots to the coefficients of the trinomial.

x_1, x_2

roots

a, b, c

coefficients

They let you find the sum and product of the roots without computing them — useful for checking solutions or when the roots are "nice".

Problems about the sum/product of roots, checking results, choosing parameters.

State the sum and product of the roots of the equation

x^2-5x+6=0

Substitution

a=1

b=-5

c=6

Result

x_1+x_2=5

x_1\cdot x_2=6

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