Question

Determinați soluțiile reale ale ecuației 2x la 2 -7x +5 =0

Answer 1

$2 {x}^{2} - 7x + 5 = 0$

$a = 2$

$b = - 7$

$c = 5$

$\Delta = {b}^{2} - 4ac$

$\Delta = {( - 7)}^{2} - 4 \times 2 \times 5$

$\Delta = 49- 40$

$\Delta = 9$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}$

$x_{1,2}=\frac{-( - 7)\pm\sqrt{9}}{2 \times 2}$

$x_{1,2}=\frac{7\pm3}{4}$

$x_{1}=\frac{7 + 3}{4}$

$x_{1}=\frac{10}{4}$

$x_{1}=\frac{5}{2}$

$x_{2}=\frac{7 - 3}{4}$

$x_{2}=\frac{4}{4}$

$x_{2}=1$

Answer 2

[tex]2x^2-7x+5 \\ =\left(2x^2-2x\right)+\left(-5x+5\right) \\ =2x\left(x-1\right)-5\left(x-1\right) \\ \\ =\left(x-1\right)\left(2x-5\right)[/tex]