Question

4) 3х^2 +12=0; 5) 5х^2 – 30=0; 6) х^2 – 5х + 6=0; 7) 2х^2 +7х–9=0; 8) 5х^2 +8х–4=0; 9) у^2 +8у+16=0; 10) –t^2– 3t+1 =0; 11) 3а^2 +а + 4=0

Answer 1

$4)3 {x}^{2} = - 12 \\ {x}^{2} = - 4$
Нет решения
$5)5 {x}^{2} = 30 \\ {x}^{2} = 6 \\ x1 = \sqrt{6} \\ x2 = - \sqrt{6}$
$6) {x}^{2} - 5x + 6 = 0 \\ d = 25 - 24 = 1 \\ x1 = \frac{5 + 1}{2} = 3$
$x2 = \frac{5 - 1}{2} = 2$
$7)2 {x}^{2} + 7x - 9 = 0 \\ d = 49 + 72 = 121 = 11$
$x1 = \frac{ - 7 - 11}{4} = - \frac{18}{4} = - 4.5 \\ x2 = \frac{ - 7 + 11}{4} = \frac{4}{4} = 1$
$8)5 {x}^{2} + 8x - 4 = 0 \\ d = 64 + 80 = 144 = 12$
$x1 = \frac{ - 8 - 12}{10} = - \frac{20}{10} = - 2$
$x2 = \frac{ - 8 + 12}{10} = \frac{4}{10} = 0.4$
$9) {y}^{2} + 8y + 16 = 0 \\ d = 64 - 64 = 0 \\ x = \frac{ - 8 + 0}{2} = - 4$
$10) - {t}^{2} - 3t + 1 = 0 \times ( - 1) \\ {t}^{2} + 3t - 1 = 0 \\ d = 9 + 4 = 13 = \sqrt{13}$
$x1 = \frac{ - 3 - \sqrt{13} }{2} \\ x2 = \frac{ - 3 + \sqrt{13} }{2}$
$11)3 {a}^{2} + a + 4 = 0 \\ d = 1 - 48 = - 47$
Нет решения