Question

Solve the equation x³ - 9x² +14x + 24 = 0 if it is given that two of its roots are in the
ratio 3:2.​

Answer 1

Answer:

Step-by-step explanation:

x³ - 9x² +14x + 24 = 0

Let the roots be 3a 2a and b

Now sum of roots

5a+b =9

Product of roots

6a²b = -24

a²b = -4

b = -4/a²

5a-4/a²=9

5a³ - 9a² -4 = 0

5a³ + a²+2a-10a²-2a -4 = 0

a(5a²+a+2)-2(5a²+a+2) = 0

(a-2)(5a²+a+2)=0

Since

5a²+a+2 >0

a-2=0

a=2

b=-1

Therefore the roots are

6 , 4 and -1

Hope it helps  

Answer 2

Answer:

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