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(x-sqrt3)^(2)(x-sqrt7)
Given the polynomial, what are its zeros?
Choose 1 answer:
(A) 
x=-sqrt3 and 
x=-sqrt7
(B) 
x=sqrt3 and 
x=sqrt7
(c) 
x=3 and 
x=sqrt7
(D) 
x=-3 and 
x=-sqrt7

(x3)2(x7) (x-\sqrt{3})^{2}(x-\sqrt{7}) \newlineGiven the polynomial, what are its zeros?\newlineChoose 11 answer:\newline(A) x=3 x=-\sqrt{3} and x=7 x=-\sqrt{7} \newline(B) x=3 x=\sqrt{3} and x=7 x=\sqrt{7} \newline(C) x=3 x=3 and x=7 x=\sqrt{7} \newline(D) x=3 x=-3 and x=7 x=-\sqrt{7}

Full solution

Q. (x3)2(x7) (x-\sqrt{3})^{2}(x-\sqrt{7}) \newlineGiven the polynomial, what are its zeros?\newlineChoose 11 answer:\newline(A) x=3 x=-\sqrt{3} and x=7 x=-\sqrt{7} \newline(B) x=3 x=\sqrt{3} and x=7 x=\sqrt{7} \newline(C) x=3 x=3 and x=7 x=\sqrt{7} \newline(D) x=3 x=-3 and x=7 x=-\sqrt{7}
  1. Factored Polynomial: Factored polynomial: (x3)2(x7)(x - \sqrt{3})^2(x - \sqrt{7})\newlineWhich equation finds the zeros for this polynomial?\newlineSet the polynomial equal to zero.\newline(x3)2(x7)=0(x - \sqrt{3})^2(x - \sqrt{7}) = 0
  2. Finding Zeros: First, consider the factor (x3)2=0(x - \sqrt{3})^2 = 0.\newlineWhat is the value of xx?\newlineTake the square root of both sides.\newlinex3=0x - \sqrt{3} = 0\newlinex=3x = \sqrt{3}
  3. Solving (x3)2=0(x - \sqrt{3})^2 = 0: Now, consider the factor (x7)=0(x - \sqrt{7}) = 0.\newlineWhat is the value of xx?\newlinex=7x = \sqrt{7}
  4. Solving (x7)=0(x - \sqrt{7}) = 0: We have found the zeros of the polynomial:\newlinex=3x = \sqrt{3}\newlinex=7x = \sqrt{7}\newlineThese are the roots of the polynomial.

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