what is the answer of 2x²+ 3x - 1

[tex] \sf \: Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.[/tex]

[tex] \sf \: 2x^{2}+3x-1=0 [/tex]

[tex] \sf \: All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.[/tex]

[tex] \sf \: x=\frac{-3±\sqrt{3^{2}-4\times 2\left(-1\right)}}{2\times 2} [/tex]

[tex] \sf \: Square 3.[/tex]

[tex] \sf \: x=\frac{-3±\sqrt{9-4\times 2\left(-1\right)}}{2\times 2} [/tex]

[tex] \sf \: Multiply -4 times 2.[/tex]

[tex] \sf \: x=\frac{-3±\sqrt{9-8\left(-1\right)}}{2\times 2} [/tex]

[tex] \sf \: Multiply -8 times -1.[/tex]

[tex] \sf \: x=\frac{-3±\sqrt{9+8}}{2\times 2} [/tex]

[tex] \sf \: Add 9 to 8.[/tex]

[tex] \sf \: x=\frac{-3±\sqrt{17}}{2\times 2} [/tex]

[tex] \sf \: Multiply 2 times 2.[/tex]

[tex] \sf \: x=\frac{-3±\sqrt{17}}{4} [/tex]

[tex] \sf \: Now solve the equation x=\frac{-3±\sqrt{17}}{4} when ± is plus. Add -3 to \sqrt{17}.[/tex]

[tex] \sf \: x=\frac{\sqrt{17}-3}{4} [/tex]

[tex] \sf \: Now solve the equation x=\frac{-3±\sqrt{17}}{4} when ± is minus. Subtract \sqrt{17} from -3.[/tex]

[tex] \sf \: x=\frac{-\sqrt{17}-3}{4} [/tex]

[tex] \sf Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{17}}{4} for x_{1} and \frac{-3-\sqrt{17}}{4} for x_{2}.[/tex]

[tex]\large\sf{» AnsWer}[/tex]

[tex] \sf \: 2x^{2}+3x-1=2\left(x-\frac{\sqrt{17}-3}{4}\right)\left(x-\frac{-\sqrt{17}-3}{4}\right) [/tex]

#CarryOnLearning

(ノ^_^)ノ