Respuesta :
Polynomial function has zeros when x=[tex]-2, \frac{3}{4} , 5[/tex] is
[tex]4x^3-15x^2-31x+30[/tex]
Given :
polynomial function has zeros when x= -2, 3/4, 5
Lets write the zeros in factor form
If 'a' is a zero , then factor is (x-a)
The given zeros are [tex]-2, \frac{3}{4} , 5[/tex]
lets write all the three zeros in factor form
[tex](x-(-2)) (x-\frac{3}{4})(x-5)\\(x+2)(4x-3)(x-5)[/tex]
Now multiply the parenthesis to get the polynomial
[tex]\left(x+2\right)\left(4x-3\right)\left(x-5\right)\\\left(4x^2+5x-6\right)\left(x-5\right)\\4x^2x+4x^2\left(-5\right)+5xx+5x\left(-5\right)-6x-6\left(-5\right)\\combine \; like \; terms\\4x^3-15x^2-31x+30[/tex]
polynomial function has zeros when x= -2, 3/4, 5 is
[tex]4x^3-15x^2-31x+30[/tex]
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