Question

Which of the following shows an equivalent form of the equation t²+5t-24=0?

a.(t + 8)(t - 3) = 0
b.(t - 8)(t + 3) = 0
c.(t - 8)(t - 3) = 0

Answer 1

From what I remember about this the answer should be a

Answer 2

Answer: The answer is (a) (t + 8)(t - 3).

Step-by-step explanation:  We are to select the correct equation out of the given  options which is equivalent to the equation t² + 5t -24 = 0.

The first equation is

$(t+8)(t-3)=0\\\\\Rightarrow t^2+8t-3t-24=0\\\\\Rightarrow t^2+5t-24=0.$

Since it matches with the given equation, so this option is correct.

The second equation is

$(t-8)(t+3)=0\\\\\Rightarrow t^2-8t+3t-24=0\\\\\Rightarrow t^2-5t-24=0.$

Since it does not match with the given equation, so this option is incorrect.

The third equation is

$(t-8)(t-3)=0\\\\\Rightarrow t^2-8t-3t+24=0\\\\\Rightarrow t^2-11t+24=0.$

Since it does not match with the given equation, so this option is incorrect.

Thus, the correct option is (a). (t+8)(t-3)=0.