Answer:
1 + 1.58i , 1 - 1.58i
Step-by-step explanation:
2x^2=4x-7
2x^2 - 4x + 7 = 0
x = [-(-4) +/- sqrt((-4)^2 - 4 * 2 * 7 )] / 2*2
= [ 4 +/- sqrt (16 - 56)] / 4
= [4 +/- sqrt (-40) ] / 4
= 1 +/- 6.32i / 4
= 1 + 1.58i and 1 - 1.58i (answer).
Answer:
[tex]\boxed{x = 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]
Step-by-step explanation:
2x² = 4x - 7
2x² - 4x + 7 =0
a = 2; b = -4; c = 7
[tex]y =\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
[tex]=\frac{4\pm\sqrt{(-2)^2-4\times2\times7}}{2\times2}\\[/tex]
[tex]= 1 \pm\frac{\sqrt{16-56}}{4}\\[/tex]
[tex]= 1 \pm\frac{\sqrt{-40}}{4}\\[/tex]
[tex]= 1 \pm\frac{2i\sqrt{10}}{4}\\[/tex]
[tex]= 1 \pm\frac{i\sqrt{10}}{2}\\[/tex]
[tex]= 1 \pm i\sqrt{\frac{10}{4}}\\[/tex]
[tex]\boxed{= 1 \pm i\sqrt{\frac{5}{ 2}} }\\[/tex]
The graph of y = 2x² - 4x + 7 has a minimum at (1, 5). It never touches the x-axis, so both roots are imaginary.
