Question
Determine the discriminant of \( 0=2 x^{2}+4 x+10 \)
Ask by Logan Smith. in South Africa
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The discriminant is -64.
Solution
1. The discriminant \( \Delta \) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by:
\[
\Delta = b^2 - 4ac
\]
2. For the equation \( 0 = 2x^2 + 4x + 10 \), we identify:
\[
a = 2, \quad b = 4, \quad c = 10
\]
3. Substituting these values into the formula for the discriminant:
\[
\Delta = 4^2 - 4 \cdot 2 \cdot 10
\]
4. Calculating the values:
\[
\Delta = 16 - 80
\]
5. Simplifying, we find:
\[
\Delta = -64
\]
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Simplify this solution Beyond the Answer
The discriminant of a quadratic equation in the form \( ax^2 + bx + c = 0 \) can be found using the formula \( D = b^2 - 4ac \). For the equation \( 0 = 2x^2 + 4x + 10 \), the coefficients are \( a = 2 \), \( b = 4 \), and \( c = 10 \). Plugging these values into the formula gives: \[ D = 4^2 - 4(2)(10) = 16 - 80 = -64. \] Since the discriminant is negative (\( D = -64 \)), this means the quadratic equation has no real solutions, but it does have two distinct complex solutions. So, the discriminant is \( -64 \).
