Answer
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 $x$
Work Step by Step
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)
$b^2-4ac$
$(-7)^2-4*2*-3$
$49+24$
$73$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-7)±\sqrt {(-7)^2-4*2*-3})/2*2$
$x=(-(-7)±\sqrt {73})/4$
$x=(7±\sqrt {73})/4$
$x=(7±8.54)/4$
$x=(7+8.54)/4$
$x=15.54/4 = 3.885$
$x=(7-8.54)/4$
$x=-1.54/4 = -.385$
