katymarianieM
Answered

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

Verified Answer :

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 - 442 equal to 36 - 32 or equal to 4.

Answer:

 \(x=-1,\frac{-1}{2}\)

Step-by-step explanation:

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

\(D=b^2-4ac>0\)  which gives us the real and distinct roots

We have been given an equation:

\(4x^2+6x+2=0\)

Here, on comparing it with general quadractic equation which is: \(ax^2+bx+c=0\)

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

On substituting the values in the formula to find D

\(D=6^2-4(4)(2)\)

\(D=36-32\)

\(D=4\)

Now, to find x:

we have a formula:

\(x=\frac{-b\pm\sqrt{D}}{2a}\)

On substituting the values we get:

\(x=\frac{-6\pm\sqrt{4}}{2(4)}\)

\(\x=frac{-6\pm2}{8}\)

On simplification:

\(x=\frac{-8}{8},\frac{-4}{8}\)

\(x=-1,\frac{-1}{2}\)


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