4.9 Homework: solving quadratic equations

${\mathrm{2x}}^2-\mathrm{5x}-3=0$

• a Solve by factoring
• b Solve by completing the square
• c Solve by using the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4\text{ac}}}{\mathrm{2a}}$
• d Which way was easiest? Which way was hardest?
• e Check your answers by plugging back into the original equation.

$x^2-\mathrm{5x}+\text{30}=5(x+1)$

${\mathrm{3x}}^2+\text{24}x+\text{60}=0$

$\frac{2}{3}{x}^2+8\text{.}\mathrm{5x}=\mathrm{\pi x}$

$x^2-x=0$

${\mathrm{9x}}^2=\text{16}$

Consider the equation $x^2+\mathrm{8x}+c=0$ where $c$ is some constant. For what values of $c$ will this equation have…

• a Two real answers?
• b One real answer?
• c No real answers?

Starting with the generic quadratic equation ${\text{ax}}^2+\text{bx}+c=0$ , complete the square and derive the quadratic formula. As much as possible, do this without consulting your notes.