Question

Determine o valor delta ∆ nas equações abaixo:
a) x 2-4x+3=0
b)x2-8x+15=0
c)3x2-9x-6=0
d)x2-7x+12=0​

Answer 1

a)

$\large \boxed{ \begin{array}{l} \rm \: x {}^{2} - 4x + 3 = 0 \\ \\ \Rightarrow \begin{cases} \rm \: a = 1 \\ \rm \: b = - 4 \\ \rm \: c = 3\end{cases} \\ \\ \rm \Delta = ( - 4) {}^{2} - 4.1.3 \\ \Delta = 16 - 12 \\ \boxed{\Delta = 4} \checkmark \end{array}}$

b)

$\large \boxed{ \begin{array}{l} \rm \: x {}^{2} - 8x + 15 = 0 \\ \\ \Rightarrow \begin{cases} \rm \: a = 1 \\ \rm \: b = - 8 \\ \rm \: c = 15\end{cases} \\ \\ \rm\Delta = ( - 8) {}^{2} - 4.1.15 \\ \Delta = 64 - 60 \\ \boxed{\Delta = 4} \checkmark\end{array}}$

c)

$\large \boxed{ \begin{array}{l} \rm \: 3x {}^{2} - 9x - 6 = 0 \\ \\ \Rightarrow \begin{cases} \rm \: a = 3 \\ \rm \: b = - 9 \\ \rm \: c = - 6\end{cases} \\ \\ \Delta = ( - 9) {}^{2} - 4.3.( - 6) \\ \Delta = 81 + 72 \\ \boxed{\Delta = 153} \checkmark\end{array}}$

d)

$\large \boxed{ \begin{array}{l} \rm \: x {}^{2} - 7x + 12 = 0 \\ \\ \Rightarrow \begin{cases} \rm \: a = 1 \\ \rm \: b = - 7 \\ \rm \: c = 12\end{cases} \\ \\ \Delta = ( - 7) {}^{2} - 4.1.12 \\ \Delta = 49 - 48 \\ \boxed{\Delta = 1} \checkmark\end{array}}$