Question

The sum of three numbers in A.P. is -3, and their product is 8. The numbers are:

• A. -4, -1, 2
• B. -4, 0, 2
• C. -2, 1, 4
• D. -4, -2, 1

Answer 1

The correct option is A -4, -1, 2

Let the three numbers in A.P. are a-d, a, a+d.
Sum = -3
a - d + a + a + d = -3
3a = -3
a = -1

$(a-d)a(a+d)=8\Rightarrow (-1-d)\times (-1)\times (-1+d)=8\Rightarrow (1+d)(-1+d)=8\Rightarrow d^2-1=8\Rightarrow d^2=9\Rightarrow d=\pm 3\mathrm{If}d=3\mathrm{Numbers}\mathrm{are}-1-3,-1,-1+3=-4,-1,2\mathrm{If}d=-3\mathrm{Numbers}\mathrm{are}-1-(-3),-1,-1+(-3)=2,-1,-4$