Question

Tìm GTLN của mỗi đa thức sau : a , B(x) = -x^2 + 3x -7 . b, C(x) = -x ^ 2 + 7x - 20 . Q(x)= -x^2 - x + 7

Answer 1

a: \(B\left(x\right)=-\left(x^2-3x+7\right)\)

\(=-\left(x^2-3x+\dfrac{9}{4}+\dfrac{19}{4}\right)\)

\(=-\left(x-\dfrac{3}{2}\right)^2-\dfrac{19}{4}\le-\dfrac{19}{4}\)

Dấu '=' xảy ra khi x=3/2

b: Ta có: \(C\left(x\right)=-x^2+7x-20\)

\(=-\left(x^2-7x+20\right)\)

\(=-\left(x^2-7x+\dfrac{49}{4}+\dfrac{31}{4}\right)\)

\(=-\left(x-\dfrac{7}{2}\right)^2-\dfrac{31}{4}\le-\dfrac{31}{4}\)

Dấu '=' xảy ra khi x=7/2