Question

A)X² -10x +21 = 0
B)X² +13 +30 = 0
C)X² -7x - 18 = 0
D)X² +13x -30 = 0
E)2X² -x +1 = 0
F) 15 X² +2x -1 = 0

Answer 1

$a)x {}^{2} - 3x - 7x + 21 = 0 \\ x \times (x - 3) - 7(x - 3) = 0 \\ (x - 3) \times (x - 7) = 0 \\ x - 7 = 0 \\ x - 3 = 0 \\ x {}^{ {}^{1} } = 3 \\ x {}^{ {}^{2} } = 7$

$b)x {}^{2} + 43 = 0 \\ x {}^{2} = - 43 \\ \: XER$

$c)x {}^{2} + 2x - 9x - 18 = 0 \\ x \times (x + 2) - 9(x + 2) = 0 \\ (x + 2) \times (x - 9) = 0 \\ x + 2 = 0 \\ x - 9 = 0 \\ x {}^{1} = - 2 \\ x {}^{2} = 9$

$d)x {}^{2} + 15x - 2x - 30 = 0 \\ x \times (x + 15) - 2(x + 15) = \\ (x + 15) \times (x - 2) = 0 \\ x + 15 = 0 \\ x - 2 = 0 \\ x {}^{1} = - 15 \\ x {}^{2} = 2$

$e)x = \frac{ - ( -1) ± \sqrt{( - 1) { }^{2 } - 4 \times 2 \times 1 } }{2 \times 2} \\ x = \frac{1± \sqrt{1 - 8} }{4} \\ x = \frac{1± \sqrt{ - 7} }{4} \\ \: XER$

$f)15x {}^{2} + 5x - 3x - 1 = 0 \\ 5x \times (3x + 1) - (3x + 1) = 0 \\ (3x \times 1) \times (5x - 1) = 0 \\ 3x + 1 = 0 \\ 5x - 1 = 0 \\ x {}^{1} = - \frac{1}{3} \\ x {}^{2} = \frac{1}{5}$

Espero ter ajudado!!!