If f(x) = x^3 – 10x^2 + 29x – 30 and f(6) = 0, then find all of the zeros of f(x) algebraically.
1 answer:
Step 1: 1
(((x3) - (2•5x2)) + 29x) - 30 = 0
Step 2 2.1 x3-10x2+29x-30 is not a perfect cube
Step 3 Factoring: x3-10x2+29x-30
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 29x-30
Group 2: -10x2+x3
Pull out from each group separately :
Group 1: (29x-30) • (1)
Group 2: (x-10) • (x2)
(((x3) - (2•5x2)) + 29x) - 30 = 0
Step 2 2.1 x3-10x2+29x-30 is not a perfect cube
Step 3 Factoring: x3-10x2+29x-30
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 29x-30
Group 2: -10x2+x3
Pull out from each group separately :
Group 1: (29x-30) • (1)
Group 2: (x-10) • (x2)
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Part 1) <span>Given the two points (-24,7) and (30,25) a. What is an equation passing through the points?
step 1
find the slope m
m=(y2-y1)/(x2-x1)----></span>m=(25-7)/(30+24)----> m=18/54----> m=1/3
step 2
wit m=1/3 and the point (30,25)
find the equation of the line
y-y1=m*(x-x1)-----> y-25=(1/3)*(x-30)--->y=(1/3)*x-10+25
y=(1/3)*x+15
the answer Part 1) is
y=(1/3)*x+15
Part 2) <span>Is (51, 33) also on the same line?
</span>if the point (51.33) is on the line y=(1/3)*x+15
then
for x=51 the value of y must be 33
for x=51
y=(1/3)*51+15----> y=17+15----> y=32
32 is not 33
so
<span>the point does not belong to the given line
</span>
the answer Part 2) is
the point does not belong to the given line
see the attached figure
step 1
find the slope m
m=(y2-y1)/(x2-x1)----></span>m=(25-7)/(30+24)----> m=18/54----> m=1/3
step 2
wit m=1/3 and the point (30,25)
find the equation of the line
y-y1=m*(x-x1)-----> y-25=(1/3)*(x-30)--->y=(1/3)*x-10+25
y=(1/3)*x+15
the answer Part 1) is
y=(1/3)*x+15
Part 2) <span>Is (51, 33) also on the same line?
</span>if the point (51.33) is on the line y=(1/3)*x+15
then
for x=51 the value of y must be 33
for x=51
y=(1/3)*51+15----> y=17+15----> y=32
32 is not 33
so
<span>the point does not belong to the given line
</span>
the answer Part 2) is
the point does not belong to the given line
see the attached figure