Question

write a polynomial with zero 2and-1

Answer 1

Hey friend...!! here'z your answer
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Sum of zeroes = 2
Product of zeroes = -1

Formula ==>

${x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes)$
${x}^{2} - (2)x + ( - 1) = 0 \\ {x}^{2} - 2x - 1 = 0$
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#Hope its help you dear#
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Answer 2

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function.

We have two unique zeros: −2 and 4. However, −2 has a multiplicity of 2, which means that the factor that correlates to a zero of −2 is represented in the polynomial twice.

Follow the colors to see how the polynomial is constructed:

zero at −2, multiplicity 2 
zero at 4, multiplicity 1

p(x)=(x−(−2))2(x−4)1

Thus,

p(x)=(x+2)2(x−4)

Expand:

p(x)=(x2+4x+4)(x−4)

p(x)=x3−12x−16

We can graph the function to understand multiplicities and zeros visually:

The zero at x=−2 "bounces off" the x-axis. This behavior occurs when a zero's multiplicity is even.

The zero at x=4 continues through the x-axis, as is the case with odd multiplicities.