Question

The roots of a quadratic equation ax2+bx+c=0 are 3+sqrt2 and 3−sqrt2. Find the values of b and c assuming that a=1.

Answer 1

`b=-6\\c=7`

Explanation:

we know that

The general equation of a quadratic function in factored form is equal to

`y=a(x-x_1)(x-x_2)`

where

a is a coefficient of the leading term

x_1 and x_2 are the roots

we have

`a=1\\x_1=3+√(2)\\x_2=3-√(2)`

substitute

`y=(1)(x-(3+√(2)))(x-(3-√(2)))`

Applying the distributive property convert to expanded form

`y=x^2-x(3-√(2))-x(3+√(2))+(3+√(2))(3-√(2))`

`y=x^2-(3x-x√(2))-(3x+x√(2))+(9-2)`

`y=x^2-3x+x√(2)-3x-x√(2)+7`

`y=x^2-6x+7`

therefore

`b=-6\\c=7`