Question

The ratio of the roots of the equation x2 + ax + a + 2 = 0 is 2. Find the value of
parameter a

Answer 1

Step-by-step explanation:

Let a and b be root of equation

b

a

=2

a=2b

sum of roots = −α

2b+b=−α

3b=−α

b=

3

−α

Product of roots = α+2

b×2b=α+2

2b

2

=α+2

2b

2

=−3b+2

2b

2

+3b−2=0

2b

2

+4b−b−2=0

2b(b+2)−1(b+2)=0

b=−2 or b=

2

+1

If b=−2

α=−3×−2

α=6

If b=

2

1

α=−3×

2

1

α=

2

−3

Answer 2

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