Quadratic Formula
Flashcard
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.
2.
FLASHCARD QUESTION
Front
What are the coefficients in a quadratic equation?
Back
In a quadratic equation of the form ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.
3.
FLASHCARD QUESTION
Front
How do you identify a, b, and c in the equation x² - 6x + 14?
Back
In the equation x² - 6x + 14, a = 1, b = -6, and c = 14.
4.
FLASHCARD QUESTION
Front
What does the discriminant (b² - 4ac) tell us about the roots of a quadratic equation?
Back
The discriminant indicates the nature of the roots: if it is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if it is negative, there are no real roots (the roots are complex).
5.
FLASHCARD QUESTION
Front
How do you solve the quadratic equation 8x² - 6x = -1?
Back
First, rearrange to 8x² - 6x + 1 = 0. Then apply the quadratic formula with a = 8, b = -6, c = 1.
6.
FLASHCARD QUESTION
Front
What are the roots of the quadratic equation x² + 4x + 3 = 0?
Back
The roots can be found using the quadratic formula: x = (-4 ± √(4² - 4*1*3)) / (2*1) = -1 and -3.
7.
FLASHCARD QUESTION
Front
What is the significance of the '±' symbol in the quadratic formula?
Back
The '±' symbol indicates that there are two possible solutions for x, one for addition and one for subtraction.
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