Question

Create a polynomial with the following attributes:

* degree is 3
* zeros are -2, 4, and 7

Answer 1

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Zeros :

$x = - 2$

$x = 4$

$x = 7$

Thus ;

$x + 2 = 0$

$x - 4 = 0$

$x - 7 = 0$

Multiply above equations :

$(x + 2)(x - 4)(x - 7) = 0$

Expand

$( {x}^{2} - 2x - 8)(x - 7) = 0$

${x}^{3} - 7 {x}^{2} - 2 {x}^{2} + 14x - 8x + 56 = 0$

${x}^{3} - 9 {x}^{2} + 6x + 56 = 0$

$y = f(x) = {x}^{3} - 9 {x}^{2} + 6x + 56$

Done...

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