Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots sqrt 5 and 2?
A)f(x)=3x^3-6x^2-15x+30. B)f(x)=x^3-2x^2-5x+10. C)f(x)=3x^2-21x+30. D)f(x)=x^2-7x+10.

Answer 1

The polynomial functions A) and C) have a leading coefficient of 3, but C) has a lower degree.
f ( x ) = 3 x² - 21 x + 30
3 ( x² - 7 x + 10 ) = 3 ( x² - 5 x - 2 x + 10 ) =
= 3 ( x ( x - 5 ) - 2 ( x - 5 )) = 3 ( x - 2 ) ( x - 5 ) = 0
x = 2 and x = 5 ( roots )
Answer:
C ) f ( x ) = 3 x² - 21 x + 30