## Algebra 1

a) 16; $x= 1, 5$ b) 81; $x= -5, 4$ c) 73, $x= 3.89, -.39$ d) rational--parts a and b had perfect squares for determinants and had rational values for $x$
a) $b^2-4ac$ $(-6)^2-4*1*5$ $36-20$ $16$ $x^2-6x+5=0$ $(x-5)(x-1)=0$ $x-5 = 0$ $x-5+5 = 0+5$ $x = 5$ $x-1 = 0$ $x-1+1 = 0+1$ $x = 1$ b) $b^2-4ac$ $1^2-4*1*-20$ $1-(-80)$ $81$ $x^2+x-20=0$ $(x+5)(x-4)=0$ $x+5=0$ $x+5-5=0-5$ $x=-5$ $x-4=0$ $x-4+4=0+4$ $x = 4$ c) $b^2-4ac$ $(-7)^2-4*2*-3$ $49+24$ $73$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-(-7)±\sqrt {(-7)^2-4*2*-3})/2*2$ $x=(-(-7)±\sqrt {73})/4$ $x=(7±\sqrt {73})/4$ $x=(7±8.54)/4$ $x=(7+8.54)/4$ $x=15.54/4 = 3.885$ $x=(7-8.54)/4$ $x=-1.54/4 = -.385$