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3 years ago

B^2+ 8b + 12 = (b + 6) (?) find the other binomial which will complete the factorization

Mathematics

2 answers:

Naya [18.7K]3 years ago

7 0

Answer:

Step-by-step explanation:

natima [27]3 years ago

7 0

Answer:

Step-by-step explanation:

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here we gonna use a rule:

if x1 and x2 are rooots of the quadratic equation: ax² + bx + c = 0

then x1 + x2 = -b/a

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b^2+ 8b + 12 = (b - b1) (b - b2)

This prove that “b1 = -6” is a root of the quadratic equation b^2+ 8b + 12 = 0

since, the sum of roots b1 + b2 = -8/1 = -8 then b2 = -8 - b1 = -8 - (-6) = -2

then

b^2+ 8b + 12 = (b - (-6)) (b - (-2))

= (b + 6) (b+ 2).

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astra-53 [7]

Given:

The given equation is:

$-3t^2+24t=h$

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

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Solution:

We have,

$-3t^2+24t=h$

The height of the ball is at least 36 feet above the ground. It means $h\geq 36$ .

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Splitting the middle term, we get

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The critical points are:

$-3(t-2)(t-6)=0$

$t=2,6$

These two points divide the number line in 3 intervals $(-\infty,2),(2,6),(6,\infty)$ .

Intervals Check point $-3(t-2)(t-6)\geq 0$ Result

$(-\infty,2)$ 0 $(-)(-)(-)=(-)$ False

$(2,6)$ 4 $(-)(+)(-)=+>0$ True

$(6,\infty)$ 8 $(-)(+)(+)=(-)$ False

The inequality is true for (2,6) and the sign of inequality is $\geq$ . So, the ball is above 36 feet between 2 to 6 seconds.

$6-2=4$

Therefore, the required inequality is $-3t^2+24t\geq 36$ and the ball is 36 feet above for 4 seconds.

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