Question

100x^2-100x+25=0 é igual a 1/2??​

Answer 1

Resposta:

Sim, x=0,5 é uma raiz dupla e igual.

Explicação passo-a-passo:

100x²-100x+25=0 (÷25)

4x²-4x+1=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~4x^{2}-4x+1=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=4{;}~b=-4~e~c=1\\\\\Delta=(b)^{2}-4(a)(c)=(-4)^{2}-4(4)(1)=16-(16)=0\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-4)-\sqrt{0}}{2(4)}=\frac{4-0}{8}=\frac{4}{8}=0,5\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-4)+\sqrt{0}}{2(4)}=\frac{4+0}{8}=\frac{4}{8}=0,5\\\\S=\{0,5,~0,5\}$