Answer:
Roots x = -1 and x =5
k(x) = (x + 1)(x - 5)
m(x) = 1/2(x + 1 )(2x - 10)
Roots x = 1 and x = -5
n(x) = (3x + 15)(x - 1)
f(x) = (x - 1)(x + 5)
q(x) = (2x - 2)(3x + 15)
Neither
h(x) = 1/2(x + 1)(2x - 20)
Step-by-step explanation:
We have given that ,the quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.
1. Write root as factor changing the sign and put each factor in paranthesis
2.Multiply paire of roots together using box to find the multiplication
3.Make sure that each factor multiplied by every other factor.
The function has roots x = -1 and x =5
[tex]k(x) = (x + 1)(x - 5)\\\\k(x)=x^2-5x+x-5\\k(x)=x^2-4x-5\\[/tex]
[tex]m(x) = 1/2(x + 1 )(2x - 10)\\m(x)=1/2(2x^2-10x+2x-10)\\m(x)=1/2(2x^2-8x-10)\\m(x)=x^2-4x-5[/tex]
The function k(x) and m(x) has root x=-5 and x=5
The function has roots x = 1 and x = -5
[tex]n(x) = (3x + 15)(x - 1)\\n(x)=3x^2-3x+15x-15\\n(x)=3x^2+12x-15\\n(x)=1/3(x^2+4x-5)[/tex]
[tex]f(x) = (x - 1)(x + 5)\\f(x)=x^2+5x-x-5\\f(x)=x^2+4x-5[/tex]
[tex]q(x) = (2x - 2)(3x + 15)\\q(x)=6x^2+30x-6x-30\\q(x)=6x^2+24x-30\\q(x)=1/6(x^2+4x-5)[/tex]
The function n(x),q(x) and f(x) has roots x=1 and x=-5
h(x) = 1/2(x + 1)(2x - 20)
h(x) has no roots from roots at x=−1 and x=5, and x=1 and x=−5.
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