victoriagentryp5837x victoriagentryp5837x
  • 08-03-2018
  • Mathematics
contestada

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots square root of 5 and 2?

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JannetPalos
JannetPalos JannetPalos
  • 06-10-2018

Since there are two zeroes, the polynomial function of lowest degree is a quadratic polynomial.

Let it be p(x).

So, [tex]p(x) = (x-\sqrt{5})(x-2)[/tex]

Note that the leading coefficient should be 3.

Therefore, [tex]p(x) = 3(x-\sqrt{5} )(x-2)[/tex]

[tex]=3[x^{2}-(2+\sqrt{5})x+2\sqrt{5}  ][/tex]

[tex]=3x^{2}-3(2+\sqrt{5})x+6\sqrt{5}[/tex]

Answer Link
buddyhanstein buddyhanstein
  • 02-07-2020

Answer:

the polynomial is: 3x^2-21x+30

Step-by-step explanation:

go it right on edge

Answer Link

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