Vamos determinara equação do 2o grau, na incógnita x, cujas raízes são os números reais seguintes:a) 7 e 12 b) - 10 e - 3 c) 4/7 e - 3 d) 9 e - 6 e) -

a)

\[\eqalign{ & \left( {x - 7} \right)\left( {x - 12} \right) = 0 \cr & {x^2} - 7x - 12x + 84 = 0 }\]

b)

\[\eqalign{ & \left( {x - \left( { - 10} \right)} \right)\left( {x - \left( { - 3} \right)} \right) = 0 \cr & \left( {x + 10} \right)\left( {x + 3} \right) = 0 \cr & {x^2} + 10x + 3x + 30 = 0 \cr & {x^2} + 13x + 30 = 0 }\]

c)

\[\eqalign{ & \left( {x - \dfrac{4}{7}} \right)\left( {x - \left( { - 3} \right)} \right) = 0 \cr & \left( {x - \dfrac{4}{7}} \right)\left( {x + 3} \right) = 0 \cr & {x^2} + 3x - \dfrac{4}{7}x - \dfrac{{12}}{7} = 0 \cr & {x^2} + \dfrac{{17x}}{7} - \dfrac{{12}}{7} = 0 }\]

d)

\[\eqalign{ & \left( {x - 9} \right)\left( {x - \left( { - 6} \right)} \right) = 0 \cr & \left( {x - 9} \right)\left( {x + 6} \right) = 0 \cr & {x^2} - 9x + 6x - 54 = 0 \cr & {x^2} - 3x - 54 = 0 }\]

e)

\[\eqalign{ & \left( {x - 8} \right)\left( {x - \left( { - 8} \right)} \right) = 0 \cr & \left( {x - 8} \right)\left( {x + 8} \right) = 0 \cr & {x^2} - 8x + 8x - 64 = 0 \cr & {x^2} - 64 = 0 }\]

f)

\[\eqalign{ & \left( {x - 0} \right)\left( {x - \left( { - \dfrac{4}{9}} \right)} \right) = 0 \cr & \left( x \right)\left( {x + \dfrac{4}{9}} \right) = 0 \cr & {x^2} + \dfrac{4}{9}x = 0 }\]