Question

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:

2x2 + 7x + 3 = 0

Answer 1

\[D= b^2-4ac\] tells you if there are solutions in \(\mathbb{R}  \text{or in } \mathbb{C}\)

Answer 2

if \[ D > 0 \longrightarrow \text{two solutions in} \ \mathbb{R} \] if
\[D =0 \longrightarrow \text{only one solution in } \ \mathbb{R}\] and for \[D< 0 \longrightarrow \text{no solutions in } \mathbb{R}\]

Answer 3

It says i need a numerical answer.

Answer 4

\[ D = 7^2-4 \cdot 2 \cdot 3 = 25 \] so how many solutions do you expect?

Answer 5

But is that the final answer?

Answer 6

somehow yes, if you know how to read it, it's a positive value, hence you know that there are two solutions to this quadratic equations, when there are two solutions to a quadratic equations -> the two roots, you can express it in its factored form.

Answer 7

But it doesnt give me an option for two solutions.

Answer 8

\[ p(x) = \left(x+\frac{1}{2}\right)( x+3) =(2x+1)(x+3)\]

Answer 9

that's the factored form, obtained by solving the quadratic equation.

Answer 10

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Answer 11

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:

Answer 12

So if that is the question, then ONLY the middle term
\[ D= b^2-4ac\] will tell you if the quadratic formula can be factored.

Answer 13

it's value is 25

Answer 14

I guess that's the answer then, but I always have problems with such questions when they intend on something so specific (-: but that's how quadratic equations work anyway. the b^2-4ac term decides about whether you can factor it out or not.

Answer 15

so the answer is 25?

Answer 16

that's the only numerical answer you can obtain by the with the equations given above, applied on the functions, so I would say yes.

Answer 17

Thank you!