how to write a quadratic equation in the form (ax^2+bx+c=0) with given roots?
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
- MsMathLv 71 decade agoFavorite Answer
Subtract each root from x, and then multiply
= 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)
= x^2 - 6x + 9 - 2
= x^2 - 6x + 7
- mr greenLv 41 decade ago
given quadratic equation, solutions can be found by quadratic formula.
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...