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how to determine a quadratic equation given the roots or given the sum and product of the roots

Sagot :

Jadecapalacidn
given the roots:
for example you are given 2 and 3 as the roots of your quadratic equation.

that means x=2 and x=3

transpose the constant to the other side

(x-2)  and (x-3)

remember when you are transposing, you will change the sign to it's opposite.

after that, multiply (x-2)(x-3)

it will result to [tex]x^2-5x+6[/tex]

if the given root is a fraction. cross multiply

x=[tex] \frac{1}{2} [/tex]

2x=1
(2x-1)

given sum (s) and product (p)

just use the equation below and substitute

[tex]x^2-sx+p=0[/tex]

example:

write a quadratic equation knowing the the sum of its roots is 8 and its product is 16.

then s=8 and p=16

[tex] x^{2} -8x+16=0[/tex]
here's the formula x^2-sumx+product
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