Q:

Use a quadratic equation to find two real numbers with the sum of 2 and a product of -24

Accepted Solution

A:
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 = -24or,  k x  (2-k)  =  -24or, [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 = -4Now, if k = 6, then other number is ( 2 - k ) = -4And if k = -4, then other number is ( 2-k) = -6Hence, the two real numbers with the sum of 2 and a product of -24  is 6 and -4.