Question

equações de 2 grau

a-)1x² -5x+6=0



b-)2x²+3x-5=0

Answer 1

a

$d \: = delta \\ \\ d = {b}^{2} - 4ac \\ \\ d = ( { - 5})^{2} - 4 \times 1 \times 6 \\ d = 25 - 24 \\ d = 1 \\ \\ x = \frac{ - b \frac{ + }{ - } \sqrt{d} }{2a} \\ x = \frac{ - ( - 5) \frac{ + }{ - } \sqrt{1} }{2 \times 1} \\ x = \frac{5 \frac{ + }{ - } 1}{2} \\ \\ {x}^{1} = \frac{5 + 1}{2} = \frac{6}{2} = 3 \\ \\ {x}^{2} = \frac{5 - 1}{2} = \frac{4}{2} = 2$

b

$d = {b}^{2} - 4ac \\ d = {3}^{2} - 4 \times 2 \times ( - 5) \\ d = 9 + 40 \\ d = 49 \\ \\ x = \frac{ - b \frac{ + }{ - } \sqrt{d} }{2 \times a} \\ x = \frac{ - 3 \frac{ + }{ - } \sqrt{49} }{2 \times 2} \\ x = \frac{ - 3 \frac{ + }{ - }7 }{4} \\ \\ {x}^{1} = \frac{ - 3 + 7}{4} = \frac{4}{4} = 1 \\ \\ {x}^{2} = \frac{ - 3 - 7}{4} = = \frac{ - 10}{4} = \frac{ - 5}{2}$