Answer:
1. [tex] {x}^{2} - 16x + 55[/tex]
2. Required factors: (x - 10) (x - 13)
x = 10, x = 13
Step-by-step explanation:
1.
Graph is intersecting x-axis at points (5, 0) & (11, 0)
Hence, x = 5 & x = 11 are zeroes of the function.
So, (x - 5) & (x - 11) are factors of the quadratic function:
Therefore, required function is:
[tex](x - 5)(x - 11) \\ = {x}^{2} - 11x - 5x + 55 \\ = {x}^{2} - 16x + 55[/tex]
2.
[tex] y = x^2 - 23x + 130[/tex]
[tex]\therefore y = x^2 - 10x -13x+ 130[/tex]
[tex]\therefore y = x(x - 10) -13(x - 10)[/tex]
[tex]\therefore y = (x - 10) (x - 13)[/tex]
Plug y = 0
So, x - 10 = 0, x - 13 =0
x = 10, x = 13
