f(x)= 2x2-3x-2 Determine the zeros of each function by factoring:

Sunday, November 21, 2010

The roots of f(x) = 2x^2-3x-2 are required.

Solve the quadratic equation 2x^2 - 3x - 2 = 0.

The roots of a quadratic equation ax^2 + bx + c = 0 are given by $\displaystyle\frac{{-{b}\pm\sqrt{{{{b}}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}$

For the equation 2x^2 - 3x - 2 = 0, a = 2, b = -3 and c = -2, the roots of the equation are:

$\displaystyle\frac{{-{\left(-{3}\right)}\pm\sqrt{{{{\left(-{3}\right)}}^{{2}}-{4}\cdot{2}\cdot-{2}}}}}{{{2}\cdot{2}}}$

$\displaystyle\frac{{{3}\pm\sqrt{{{9}+{16}}}}}{{4}}$

$\displaystyle\frac{{{3}\pm\sqrt{{25}}}}{{4}}$

$\displaystyle\frac{{{3}\pm{5}}}{{4}}$

8/4 and -2/4

2 and -1/2

The roots of f(x) = 2x^2-3x-2 are 2 and -1/2

Notes