Answer:
[tex]x^2-5x + 25 = 0[/tex]
Step-by-step explanation:
Let a, b are two numbers.
Given:
Sum of the two numbers is 5.
[tex]a+b=5[/tex]
And its product is 25.
[tex]a\times b =25[/tex]
We need to find the quadratic equation using given condition.
Solution:
A quadratic equation can be written as:
[tex]x^2-(sum\ of\ the\ roots)x + (product\ of\ the\ roots) = 0[/tex]
[tex]x^2-(a+b)x + (a\times b) = 0[/tex] -------------(1)
Substitute [tex]a+b=5[/tex] and [tex]a\times b =25[/tex] in equation 1.
[tex]x^2-(5)x + (25) = 0[/tex]
[tex]x^2-5x + 25 = 0[/tex]
Therefore, Required quadratic expression
[tex]x^2-5x + 25 = 0[/tex]
