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I need help with this-example-1
User Dgraf
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1 Answer

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Answer:

B. 3x^2 +11x -20 = 0

Explanation:

For solutions p and q, the quadratic will be

(x -p)(x -q) = 0

We notice that the leading coefficients of the offered answer choices are greater than 1, so it will be convenient to use a value that "clears fractions."

(x -4/3)(x -(-5)) = 0

3(x -4/3)(x +5) = 0 . . . . multiply by 3 to clear the fraction

(3x -4)(x +5) = 0 . . . . . . clear the fraction

3x(x +5) -4(x +5) = 0 . . use the distributive property

3x^2 +15x -4x -20 = 0 . . . . use the distributive property again

3x^2 +11x -20 = 0 . . . . collect terms

_____

The constant in the product of factors is the product of roots:

(x -p)(x -q) = x^2 -(p+q)x +pq

Here, that would mean the constant would be (4/3)(-5) = -20/3.

If we compare the above quadratic to the standard form:

ax^2 +bx +c = 0

we find that we can divide the standard form equation by 'a' to get ...

pq = c/a

That is, c/a = -20/3, so we might start looking for an answer choice that has a leading coefficient of a=3 and a constant of c=-20.

User Nick Husher
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