Question

3)Determine os valores de x para os quais a função f(x)=2x²–20x+90 fique menor que a função g(x)=9x−15 4)Fornecido o polinômio p(x) = -6x² + mx + n, se p(2) = 0 e p(–1) = –6, determine os valores de m e n.

Answer 1

3)

$2x^2-20x+90<9x-15\\\\2x^2-29x+105<0\\\\\Delta=841-840=1\\\\x=\dfrac{29\pm1}{4}\\\\\\x=7.5\ ou\ x=7\\\\\\\boxed{7<x<7.5}$

4)

$p(x)=-6x^2+mx+n\\\\\\p(2)=-6(2)^2+m(2)+n=2m+n-24=0\\\\p(-1)=-6(-1)^2+m(-1)+n=-m+n-6=-6\\\\\\\left \{ {{2m+n=24} \atop {m-n=0}} \right. \\\\\\3m=24\\\\\boxed{m=8}\\\\\boxed{n=8}$