Question

The discriminant of the quadratic equation \(2x^2 - 7x + 6 = 0\) is

• A. 1
• B. -1
• C. 27
• D. 37

Hint:

Be very careful with signs, especially when the coefficient 'b' is negative. Remember that \((-b)^2\) is always positive.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The discriminant of a quadratic equation \(ax^2 + bx + c = 0\) is a value that determines the nature of its roots.

Step 2: Key Formula or Approach:
The formula for the discriminant (\(D\)) is:
\[ D = b^2 - 4ac \]

Step 3: Detailed Explanation:
For the given equation \(2x^2 - 7x + 6 = 0\), we identify the coefficients:
\(a = 2\), \(b = -7\), \(c = 6\).
Now, substitute these values into the discriminant formula:
\[ D = (-7)^2 - 4(2)(6) \] \[ D = 49 - 48 \] \[ D = 1 \]

Step 4: Final Answer:
The discriminant of the quadratic equation is 1.