Question

The sum of three numbers in AP is -3 and their product is 8 Find the numbers

• A. $2,1,-4$.
• B. $2,1,4$.
• C. $-2,-1,-4$.
• D. $2,-1,-4$.

Answer 1

The correct option is D $2,-1,-4$.

Let three no's in AP be $a-d,a,a+d$
Given, sum of three numbers $=-3$
Therefore, $a-d+a+a+d=-3$
$\Rightarrow 3a=-3$
$\Rightarrow a=-1$
Also product of three numbers $=8$
Therefore, $(a-d)a(a+d)=8$
$\Rightarrow a(a^2-d^2)=8$
$\Rightarrow (-1)(1-d^2)=8$
$\Rightarrow 1-d^2=-8$
$\Rightarrow d^2=9$
$\Rightarrow d=3$ and $d=-3$
If $a=-1$ and $d=3$ numbers are $-4,-1,2$.
And if $a=-1$ and $d=-3$ numbers are $2,-1,-4$.