Question

Descompune in factori:  2x² - 7x + 3

Answer 1

$2x^2-7x+3 \\\\ a=2 \\ b=-7 \\ c=3 \\\\ \Delta= (-7)^2-4*2*3= 49-24\to \boxed{25} \\\\ x_1; x_2 = \frac{-(-7)+ / - \sqrt{25}}{2*2}= \frac{7+/-5}{4} \\\\ x_1=\frac{7+5}{4}=\frac{12}{4}\to\boxed{\boxed{3}} \\\\ x_2=\frac{7-5}{4}=\frac{2}{4}\to\boxed{\boxed{\frac{1}{2}}} \\\\\\ 2x^2-7x+3= 2(x-3)(x-\frac{1}{2}) \\\\\\ \boxed{2x^2-7x+3=(x-3)(2x-1)}$

Answer 2

Δ=$b^{2}$-4·a ·c=49-24=25,unde Δ=determinantul ecuatiei
x1=$\frac{-b- \sqrt{Δ} }{2·a}$=$\frac{7-5}{4}$=$\frac{1}{2}$
x2 =$\frac{-b+\sqrt{Δ} }{2·a}$= $\frac{7+5}{4}$= $\frac{12}{4}$=3
2$x^{2}$-7x+3=a(x-x1)(x-x2)=2(x-$\frac{1}{2}$)(x-4)=(2x-1)(x-3)