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  • Find all the zeros of the polynomial  if one of is zero is 1.   <div style="float:

Find all the zeros of the polynomial 3\x^2 + 10x^2 - 9x - 4 if one of is zero is 1.

 

 
 
 
 
 

Answers (1)

Given    \rightarrow    P(x) = 3x^3 + 10x^2 - 9x - 4

Given 1 is the zero of P(x).

    \Rightarrow (x-1) is the one factor of P(x)

                

    \Rightarrow P(x) = (x-1)(3x^2 + 13x + 4)

    Now, lets find the zeros of 3x^2 + 13x + 4

            \Rightarrow 3x^2 + 13x + 4

            \Rightarrow 3x^2 + 12x + x+ 4\qquad (\therefore 4\times 3 = 12 \times 1)

            \Rightarrow 3x(x + 4)+1(x + 4)

            \Rightarrow (x +4)(3x+1)

            \Rightarrow x = -4    OR    \Rightarrow x = \frac{-1}{3}

All the zeros of P(x) are = 1, \frac{-1}{3}, -4

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Safeer PP

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