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If 5 and 7 are the roots of the equation | array ccc x & 4 & 5 7 & x & 7 5 & 8 & x array |=0 then what is the third root?

Options

  1. A-12
  2. B9
  3. C13
  4. D14

Correct answer

A. -12

Step-by-step solution

| array lll x & 4 & 5 7 & x & 7 5 & 8 & x array |=0 aligned & x (x^2-56 )-7(4 x-40)+5(28-5 x)=0 & x^3-56 x-28 x+280+140-25 x=0 & x^3-109 x+420=0 aligned Since 5 and 7 are the roots of the given equation so that x^2-12 x+35 is a factor of the given equation, when we divide the given equation by x^2-12 x+35 it gives x+12=0 x=-12 .

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