Answer:
[tex]b^{2}-4ac=25> 0\ for\ 2x^{2}+7x+3=0[/tex]
This shows the roots of the equation 2x² + 7x + 3 = 0 are distinct real roots .
Step-by-step explanation:
As given the expression is given in the question .
[tex]= \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
Thus the part shows the equation is factoring is represented by [tex]b^{2}-4ac[/tex] .
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 [tex]b^{2}-4ac[/tex]
[tex]= 7^{2}-4\times 2\times 3[/tex]
As
7² = 49
[tex]=49-24[/tex]
= 25
Thus
[tex]b^{2}-4ac=25> 0\ for\ 2x^{2}+7x+3=0[/tex]
This shows the roots of the equation 2x² + 7x + 3 = 0 are distinct real roots .
