Answer:
The two real numbers with the sum of 2 and a product of -24 is 6 and -4.
Step-by-step explanation:
Let on of the number is k.
⇒ The other number is ( 2 - k)
Now, product of the numbers = -24
⇒ First Number x Second Number = -24
or, k x (2-k) = -24
or, [tex]2k - k^{2} + 24 = 0 \implies k^{2} - 2k - 24 = 0[/tex]
or, [tex]k^{2} - 6k + 4k - 24 = 0 \implies k (k-6) +4(k-6) = 0[/tex]
or, (k-6)(k+4) = 0
⇒(k-6) = 0 or (k +4) = 0
⇒ k = 6 , or k = -4
Now, if k = 6, then other number is ( 2 - k ) = -4
And if k = -4, then other number is ( 2-k) = -6
Hence, the two real numbers with the sum of 2 and a product of -24 is 6 and -4.
