Question

a quadratic equation of the form 0 = ax² + bx + c has one real number solution. which could be the equation?
○ 0 = 2x² − 4x + 1
○ 0 = 2x² − 5x + 3
○ 0 = −2x² − 4x − 2
○ 0 = −2x² − 3x − 1

Explanation:

Step1: Recall discriminant formula

For quadratic \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\). One real solution when \(D = 0\).

Step2: Calculate D for first option

Option 1: \(2x^2 - 4x + 1\), \(a = 2\), \(b = -4\), \(c = 1\)
\(D = (-4)^2 - 4(2)(1) = 16 - 8 = 8
eq 0\).

Step3: Calculate D for second option

Option 2: \(2x^2 - 5x + 3\), \(a = 2\), \(b = -5\), \(c = 3\)
\(D = (-5)^2 - 4(2)(3) = 25 - 24 = 1
eq 0\).

Step4: Calculate D for third option

Option 3: \(-2x^2 - 4x - 2\), \(a = -2\), \(b = -4\), \(c = -2\)
\(D = (-4)^2 - 4(-2)(-2) = 16 - 16 = 0\). (Stop, as D=0 here.)

Answer:

\(0 = -2x^2 - 4x - 2\) (the third option)