Question

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

Answer 1

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 2

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:

$x=\frac{-8}{8},\frac{-4}{8}$

$x=-1,\frac{-1}{2}$