katymarianieM
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Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.

−b b2 − 4ac 2a

Use the part of the quadratic formula that you chose above and find its value given the following quadratic equation:

4x2 + 6x + 2 = 0

Respuesta :

meerkat18
The part of the quadratic formula tells you whether the quadratic equation can be solved by factoring is b2 - 4ac which is the determinant of the equation. in this case, the determinant of 4x2 + 6x + 2 = 0 is 6^2 - 4*4*2 equal to 36 - 32 or equal to 4. 

Answer:

 [tex]x=-1,\frac{-1}{2}[/tex]

Step-by-step explanation:

The following formula tells us that  a quadratic equation can be solved:

[tex]D=b^2-4ac>0[/tex]  which gives us the real and distinct roots

We have been given an equation:

[tex]4x^2+6x+2=0[/tex]

Here, on comparing it with general quadractic equation which is: [tex]ax^2+bx+c=0[/tex]

Here, a=4,b=6 and c=2

On substituting the values in the formula to find D

[tex]D=6^2-4(4)(2)[/tex]

[tex]D=36-32[/tex]

[tex]D=4[/tex]

Now, to find x:

we have a formula:

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

On substituting the values we get:

[tex]x=\frac{-6\pm\sqrt{4}}{2(4)}[/tex]

[tex]\x=frac{-6\pm2}{8}[/tex]

On simplification:

[tex]x=\frac{-8}{8},\frac{-4}{8}[/tex]

[tex]x=-1,\frac{-1}{2}[/tex]


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