Question

find a polynomial whose zeros are 3 and -2​

Answer 1

Step-by-step explanation:

Let the polynomial be f(x), and it's two zeros are A and B

then the polynomial is given by

f(x) = k[x² - (Sum of the zeros)x + product of the zeros] where k is a constant.

=> f(x) = k[x² - (A + B)x + AB]

Given that, two zeros are 3 and -2

Therefore,

Sum of the zeros (A + B) = 3 + (-2)

= 1

And,

Product of the zeros (AB) = 3*(-2)

= - 6

Therefore,

Required Polynomial,

f(x) = k[x² - 1x + (-6)]

f(x) = k[x² - x - 6]

Let k be 1,

So,

f(x) = x² - x - 6

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Answer 2

Answer:

x²-x-6

Step-by-step explanation:

p(x) = x²-(a+b) x+ab

=x²-(3-2)x+(3*-2)

=x²-(1)x+(-6)

=x²-x-6