Question

if 1 and -2 are two zeros of the polynomial (x³-4x²-7x+10) find iths third zero​

Answer 1

Since 1 and -2 are zeroes  (x-1)  and  (x+2) are factors of the polynomial

so (x-1)(x+2) =  $x^{2}$ +x-2 is a factor of polynomial

now divide

                    x  -5                    

   $x^{2}$  +x-2  |  $x^{3}$   -4$x^{2}$  -7x  +10

                -  $x^{3}$    - $x^{2}$    +2x

                             -5$x^{2}$  -5x   +10

                             +5$x^{2}$   +5x  -10

                                                 0

Since (x-5) is the quotient it is the other factor of  p(x).

Therefore the third zero is 5.

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