Answer:
Part A - Option B - \(b^2-4ac\)
Part B - \(b^2-4ac=25\)
Step-by-step explanation:
Part A : Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.
The formula which tells the quadratic equation can be solve by factoring is called a discriminant.
Discriminant of the quadratic equation is \(D=b^2-4ac\)
So, Option B is correct.
Part B : Use the part of the quadratic formula that you chose above and find its value given the following quadratic equation:
\(2x^2 + 7x + 3 = 0\)
The solution of the quadratic equation \(ax^2+bx+c=0\) is
\(x=\frac{-b\pm \sqrt{D}}{2a}\)
On comparing with \(2x^2 + 7x + 3 = 0\)
a=2 ,b=7 ,c=3
\(D=b^2-4ac\)
\(D=7^{2}-4(2)(3)}\)
\(D=49-24\)
\(D=25>0\)
So, there exist distinct real roots.
Substitute in the formula,
\(x=\frac{-7\pm\sqrt{25}}{4}\)
\(x=\frac{-7\pm 5}{4}\)
\(x=\frac{-7+5}{4},\frac{-7-5}{4}\)
\(x=\frac{-2}{4},\frac{-12}{4}\)
\(x=-\frac{1}{2},-3\)
