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Difficulty: EasyQuadratic Equations and the Quadratic Formula

What is the value of the discriminant of the quadratic equation 3x2+5x−2=03x^2 + 5x - 2 = 0?

Answer: 49

Answer

The discriminant of the quadratic equation is 49.
The discriminant is calculated using the formula b2−4acb^2 - 4ac. For the equation 3x2+5x−2=03x^2 + 5x - 2 = 0, the coefficients are a=3a = 3, b=5b = 5, and c=−2c = -2. Substituting these yields 52−4(3)(−2)=25−(−24)=25+24=495^2 - 4(3)(-2) = 25 - (-24) = 25 + 24 = 49.

Step-by-Step Solution

1
Identify the coefficients of the quadratic equation 3x2+5x−2=03x^2 + 5x - 2 = 0 in the standard form ax2+bx+c=0ax^2 + bx + c = 0.
a=3a = 3, b=5b = 5, and c=−2c = -2
To use the discriminant formula, we must first extract the constant coefficients corresponding to each term.
2
Substitute the coefficients into the discriminant formula D=b2−4acD = b^2 - 4ac.
D=52−4(3)(−2)=25−(−24)=25+24=49D = 5^2 - 4(3)(-2) = 25 - (-24) = 25 + 24 = 49
Calculating the value of the discriminant provides the required solution.

Key Concept

Calculating the discriminant of a quadratic equation to determine the nature of its roots.
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Topics

Quadratic Equations and the Quadratic Formula

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