Question

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:

2x2 + 7x + 3 = 0

Answer 1

`b^(2)-4ac=25> 0\ for\ 2x^(2)+7x+3=0`

This shows the roots of the equation 2x² + 7x + 3 = 0 are distinct real roots .

Explanation:

As given the expression is given in the question .

`= \frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`

Thus the part shows the equation is factoring is represented by
`b^(2)-4ac` .

Now as the quadratic equation given is

2x² + 7x + 3 = 0

As the equation in the form ax² + bx + c = 0

a = 2 , b = 7 , c = 3

Thus put all the values in
`b^(2)-4ac`

`= 7^(2)-4* 2* 3`

As

7² = 49

`=49-24`

= 25

Thus

`b^(2)-4ac=25> 0\ for\ 2x^(2)+7x+3=0`

This shows the roots of the equation 2x² + 7x + 3 = 0 are distinct real roots .