Answer:
a) The estimates for the solutions of [tex]4\cdot x^{2}-4\cdot x -1 = 0[/tex] are [tex]x_{1}\approx -0.25[/tex] and [tex]x_{2} \approx 1.25[/tex].
b) The estimates for the solutions of [tex]4\cdot x^{2}-4\cdot x -1 = 2[/tex] are [tex]x_{1}\approx -0.5[/tex] and [tex]x_{2} \approx 1.5[/tex]
Step-by-step explanation:
From image we get a graphical representation of the second-order polynomial [tex]y = 4\cdot x^{2}-4\cdot x -1[/tex], where [tex]x[/tex] is related to the horizontal axis of the Cartesian plane, whereas [tex]y[/tex] is related to the vertical axis of this plane. Now we proceed to estimate the solutions for each case:
a) [tex]4\cdot x^{2}-4\cdot x -1 = 0[/tex]
There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:
[tex]x_{1}\approx -0.25[/tex], [tex]x_{2} \approx 1.25[/tex]
b) [tex]4\cdot x^{2}-4\cdot x -1 = 2[/tex]
There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:
[tex]x_{1}\approx -0.5[/tex], [tex]x_{2} \approx 1.5[/tex]
