To solve the quadratic equation \(2a^2 - 46a + 252 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\) from the general form of a quadratic equation \(ax^2 + bx + c = 0\).
For the equation \(2a^2 - 46a + 252 = 0\):
- \(a = 2\)
- \(b = -46\)
- \(c = 252\)
The quadratic formula is given by:
\[ a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Substitute the values we identified into the formula:
\[ a = \frac{-(-46) \pm \sqrt{(-46)^2 - 4 \cdot 2 \cdot 252}}{2 \cdot 2} \]
Simplify inside the square root first:
\[ (-46)^2 = 2116 \]
\[ 4 \cdot 2 \cdot 252 = 2016 \]
So, the equation under the square root becomes:
\[ 2116 - 2016 = 100 \]
Now substitute back into the quadratic formula:
\[ a = \frac{46 \pm \sqrt{100}}{4} \]
Since \(\sqrt{100} = 10\), we have:
\[ a = \frac{46 \pm 10}{4} \]
This gives us two possible solutions:
\[ a = \frac{46 + 10}{4} \]
\[ a = \frac{46 - 10}{4} \]
Calculate each solution:
\[ a = \frac{56}{4} = 14 \]
\[ a = \frac{36}{4} = 9 \]
So the solutions to the quadratic equation \(2a^2 - 46a + 252 = 0\) are \(a = 9\) and \(a = 14\).
Thus, the correct answer is:
\[ \boxed{9, 14} \]
4.
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
2a2 − 46a + 252 = 0
18, 28
9, 14
–9, –14
–18, 28
1 answer