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

Answer:

$b=-6\\c=7$

Step-by-step 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

$a=1\\x_1=3+\sqrt{2}\\x_2=3-\sqrt{2}$

substitute

$y=(1)(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))$

Applying the distributive property convert to expanded form

$y=x^2-x(3-\sqrt{2})-x(3+\sqrt{2})+(3+\sqrt{2})(3-\sqrt{2})$

$y=x^2-(3x-x\sqrt{2})-(3x+x\sqrt{2})+(9-2)$

$y=x^2-3x+x\sqrt{2}-3x-x\sqrt{2}+7$

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

therefore

$b=-6\\c=7$