The roots of the given quadratic equation are 6 and -4.
The given quadratic equation is:
[tex](x-4)(x+2)=16[/tex]
Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].
[tex]x^{2} -2x-8=16[/tex]
[tex]x^2-2x-24=0[/tex]
[tex]x^{2} -6x+4x-24=0[/tex]
[tex]x(x-6)+4(x-6)=0[/tex]
[tex](x-6)(x+4)=0[/tex]
[tex]x=6[/tex]
[tex]x=-4[/tex]
Hence, the roots of the given quadratic equation are 6 and -4.
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Answer:
The factored form of the equation is (x + 4)(x – 6) = 0.
(option C)
