Question

Calcule o discriminante e indique se a equação tem raízes reais
a)x²-10x+21=0
b)3x²-10x-8=0
c)x²-2x+1=0
d)4x²-4x+1=0
e)3x²+5x+4=0
f)3x²+6x+4=0

Answer 1

Lembrete:

๏ $\text{O discriminante da equacao e: }\Delta =b^2-4ac$
๏ $\Delta \ \textgreater \ 0\text{ (duas raizes reais e diferentes)}$
๏ $\Delta =0\text{ (duas raizes reais e iguais)}$
๏ $\Delta \ \textless \ 0\text{ (nenhuma raizes reais)}$ 
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$\text{a) }x^2-10x+21=0\\\\\Delta =\left(-10\right)^2-4\cdot 1\cdot 21\\\Delta =100-84\\\Delta =16\text{ (duas raizes reais e diferentes)}\\\\\text{b) }3x^2-10x-8=0\\\\\Delta =\left(-10\right)^2-4\cdot 3\cdot \left(-8\right)\\\Delta =100+96\\\Delta =196\text{ (duas raizes reais e diferentes)}\\\\\text{c) }x^2-2x+1=0\\\\\Delta =\left(-2\right)^2-4\cdot 1\cdot 1\\\Delta =4-4\\\Delta =0\text{ (2 raizes reais e iguais)}\\\\\text{d) }4x^2-4x+1=0\\\\\Delta =\left(-4\right)^2-4\cdot 4\cdot 1\\\Delta =16-16$
$\Delta =0\text{ (duas raizes reais e diferentes))}\\\\\text{e) }3x^2+5x+4=0\\\\\Delta =5^2-4\cdot 3\cdot 4\\\Delta =25-48\\\Delta =-23\text{ (nenhuma raiz real)}\\\\\text{f) }3x^2+6x+4=0\\\\\Delta =6^2-4\cdot 3\cdot 4\\\Delta =36-48\\\Delta =-12\text{ (nenhuma raiz real)}$