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3 years ago

The difference between the roots of the quadratic equation x2 -14x +q =0 is 6. Find q

Mathematics

1 answer:

Irina-Kira [14]3 years ago

3 0

9514 1404 393

Answer:

q = 40

Step-by-step explanation:

When the quadratic has roots p and r, it can be factored as ...

(x -p)(x -r) = x² -(p+r)x +pr

So, the sum of the roots is 14, and their difference is 6. This lets us find the roots from ...

p + r = 14

p - r = 6

2p = 20 . . . add the two equations

p = 10

r = 14 -p = 4

The value of interest is then ...

q = pr = (10)(4)

q = 40

The graph shows the roots to be 4 and 10, as we found.

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Simplifying
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Reorder the terms:
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Solving
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Move all terms containing x to the left, all other terms to the right.

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4 years ago

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- - -

The second equation is also linear:

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- - -

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