Solve the equation 24x3 – 14x2 - 63x + 45 = 0, one root being double
another.
Answers
Answered by
2
Answer:
answr
search
What would you like to ask?
MATHS
Solve the equation 24x
3
−14x
2
−63x+45=0, one root being double another.
Share
Study later
ANSWER
Denote the roots by a,2a,b; then we have
3a+b=
12
7
,2a
2
+3ab=−
8
21
,2a
2
b=−
8
15
.
From the first two equations, we obtain
8a
2
−2a−3=0
∴a=
4
3
or −
2
1
and b=−
3
5
or
12
25
.
It will be found on trial that the values a=−
2
1
,b=
12
25
do not satisfy the third equation 2a
2
b=−
8
15
;
hence we are restricted to the values
a=
4
3
,b=−
3
5
.
Thus the roots are
4
3
,
2
3
,−
3
5
.
Similar questions