mikadaqwelcartrumi
contestada

What are the approximate solutions of 2x2 − 7x = 3, rounded to the nearest hundredth?

A: No real solutions
B: x ≈ −0.77 and x ≈ 7.77
C: x ≈ −0.39 and x ≈ 3.89
D: x ≈ −3.89 and x ≈ 0.39

Respuesta :

Edufirst
2x^2 − 7x = 3

2x^2 - 7x -3 = 0

Use the quadratic formula:

[tex]x = \frac{7+/- \sqrt{ 7^{2}-4(2)(-3)} }{(2)(2)} = [7+/-8.544]/4[/tex]

x =- 0.386 and x = 3.89

Answer option C: x = -0.39 and x = 3.89

Answer:

Option C is the correct option.

Step-by-step explanation:

The given equation is 2x² - 7x - 3 = 0

In this quadratic equation we will use quadratic formula to get the roots of x.

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

By putting values of a = 2, b = -7 and c = -3 in the quadratic formula

[tex]x=\frac{7\pm \sqrt{(-7)^{2}-4\times 2\times (-3)}}{2\times 2}[/tex]

[tex]=\frac{7\pm \sqrt{49+24}}{4}[/tex]

[tex]=\frac{7\pm \sqrt{73}}{4}[/tex]

Now we get two values for x

[tex]x=\frac{7+\sqrt{73}}{4}[/tex]

[tex]=\frac{7+8.54}{4}=3.89[/tex]

and [tex]x=\frac{7-\sqrt{73}}{4}[/tex]

[tex]=\frac{7-8.54}{4}[/tex]

[tex]=-\frac{1.54}{4}=-0.39[/tex]

Therefore option C. is the answer.

Otras preguntas