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Difficulty: EasyQuadratic Equations and the Quadratic Formula

For the quadratic equation 3x2−6x+2=03x^2 - 6x + 2 = 0, what is the value of the discriminant?

Answer: 12

Answer

The discriminant of the quadratic equation is 12.
The discriminant of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is determined by the expression b2−4acb^2 - 4ac. By substituting the coefficients a=3a = 3, b=−6b = -6, and c=2c = 2 from the given equation 3x2−6x+2=03x^2 - 6x + 2 = 0, we calculate (−6)2−4(3)(2)=36−24=12(-6)^2 - 4(3)(2) = 36 - 24 = 12.

Step-by-Step Solution

1
Identify the coefficients of the quadratic equation
a=3a = 3, b=−6b = -6, and c=2c = 2
The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0.
2
Substitute the coefficients into the discriminant formula
D=(−6)2−4(3)(2)D = (-6)^2 - 4(3)(2)
The discriminant formula is D=b2−4acD = b^2 - 4ac.
3
Simplify the expression to find the final value
36−24=1236 - 24 = 12
Squaring −6-6 gives 3636 and multiplying 4×3×24 \times 3 \times 2 gives 2424. Subtracting 2424 from 3636 gives 1212.

Key Concept

Calculating the discriminant of a quadratic equation
Estimated Time:45s
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Topics

Quadratic Equations and the Quadratic Formula

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