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Flashcards: Polynomials & Quadratics

x^2+2x-15=0

Which of the following properly lists the solutions to the equation above?

x=3, x = -5

x=-3, x=5

x=5, x=-3

x=3, x = 5

x=-3, x=-5

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Flashcards: Polynomials & Quadratics

x^2+2x-15=0

Which of the following properly lists the solutions to the equation above?

Your answer:

x=-3, x=5

Your answer:

x=5, x=-3

Your answer:

x=3, x = 5

Your answer:

x=-3, x=-5

Correct answer:

x=3, x = -5

Explanation:

The quadratic equation x^2+2x-15=0 factors to (x+5)(x-3)=0 . Remember, to solve for the solutions of a quadratic you can factor it to two parenthetical terms multiplied together, because then you can leverage the fact that anything times zero is zero. If either of those parentheticals were to equal zero, then the entire equation equals zero.

The most common place to make a mistake on quadratic problems is to properly factor as above but to not take the final step of setting each parenthetical term equal to zero. Here to solve you need to perform:

x+5 = 0 , so x=-5 is the solution to the first parentheses.

x-3=0 , so x=3 is the solution to the second parentheses.

Flashcards: Polynomials & Quadratics

What are the values of that satisfy the equation x^2+36=13x ?

x=4, x=9

x=4, x=4

x=2, x=18

x=-6, x=6

x=-9, x=-4

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Flashcards: Polynomials & Quadratics

What are the values of that satisfy the equation x^2+36=13x ?

Your answer:

x=4, x=4

Your answer:

x=2, x=18

Your answer:

x=-6, x=6

Your answer:

x=-9, x=-4

Correct answer:

x=4, x=9

Explanation:

Any time you see x^2 and terms in an equation, you're likely dealing with a quadratic or polynomial, and it is therefore likely that the best way to solve those is to move all the terms to one side of the equation to set it equal to zero. Here you can do that by subtracting 13x from both sides to arrive at the quadratic:

x^2-13x+36=0

Now your job is to factor the quadratic, looking for two values that multiply to +36 and sum to . This should lead you to a factored quadratic of:

(x-9)(x-4)=0

The final - and often missed when working under time pressure! - step is to set each parentheses equal to zero to solve the equation. This means that your solutions are:

x-9 = 0 , so x=9

x-4=0 , so x=4

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Flashcards: Polynomials & Quadratics

Flashcards: Polynomials & Quadratics

Flashcards: Polynomials & Quadratics

Flashcards: Polynomials & Quadratics

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Flashcards: Polynomials & Quadratics

Flashcards: Polynomials & Quadratics

Flashcards: Polynomials & Quadratics

Flashcards: Polynomials & Quadratics

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