Anonymous

# how to write a quadratic equation in the form (ax^2+bx+c=0) with given roots?

for example

3+root2, 3-root2 is the given roots

root is the root sign

plzz explain step by step thznkkzz

this aint a lazy hw guy here, plzz itz for examm

Relevance

Subtract each root from x, and then multiply

(x-(3+sqrt(2))) (x-(3-sqrt(2)))

FOIL

= x^2 - x(3-sqrt(2)) - x(3+sqrt(2)) + (3+sqrt(2))(3-sqrt(2))

= x^2 - 3x + x*sqrt(2) - 3x - x*sqrt(2) + 9 - 3sqrt(2) + 3sqrt(2)

- sqrt(2)*sqrt(2)

= x^2 - 6x + 9 - 2

= x^2 - 6x + 7

say the formula gave us two solutions (or roots), call them a and b.

then we can now put them in factored form of the quadratic equation...ax^2+bx+c=0 = (x-a)(x-b), so x=a or x=b.

[eg: x^2 - 3x + 2 = 0 = (x-1)(x-2), so x = 1 or x = 2.

in your case the roots are 3-Root2 and 3+Root2. the quadratic equation is:

ax^2+bx+c=0 = [x-3+Root2)][x -3-Root2)]. we must write factors like this since, x = 3 + Root2 and x=3 - Root2.

now multiply the two factors for quadratic equation in standard form...