9514 1404 393
Answer:
fill in the coefficients and evaluate the formula
x ≈ 2±√(4+3√2) ≈ {-0.871, 4.871}
Step-by-step explanation:
The quadratic formula for the solution of ...
ax² +bx +c = 0
is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The use of this formula requires that you know the values of a, b, c. You can find these by comparing the given quadratic with the standard form, above.
When you are asked for "roots" or "zeros", you are being asked for the values of x that make the polynomial have a value of zero:
x² -4x -3√2 = 0
In this form, you can see the coefficients are ...
a = 1, b = -4, c = -3√2
Using these values in the quadratic formula, you have ...
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-3\sqrt{2})}}{2(1)}=\dfrac{4\pm\sqrt{16+12\sqrt{2}}}{2}\\\\\boxed{x=2\pm\sqrt{4+3\sqrt{2}}\approx\{-0.871000, 4.871000\}}[/tex]
