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3 years ago

Which is a zero of the quadratic function f(x) = 4x2 + 24x + 11?

2 answers:

7 0

4x^2 + 24x + 11 = 0

4x^2 + 2x + 22x + 11 = 0

4x(x + 0.5) + 22(x + 0.5) = 0

(4x + 22) (x + 0.5) = 0

x+5 = 0 gives x = -0.5
and
4x + 22 = 0 gives x = -5.5

so solution set is (-0.5, -5.5)

jarptica [38.1K]3 years ago

6 0

Set to zero
0=4x^2+24x+11
factor
use ac method
muliplty 4 and 11
44
what 2 numbers multily to get 44 and ad to get 24?
2 and 22
0=4x^2+2x+22x+11
0=(4x^2+2x)+(22x+11)
0=2x(2x+1)+11(2x+1)
0=(2x+11)(2x+1)
set to zero

2x+11=0
2x=-11
x=-11/2

2x+1=0
2x=-1
x=-1/2

x=-11/2 and -1/2

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Given:

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• Time, t = 6 years

• Interest rate, r = 5.3% ==> 0.053

• Number of times compounded = quarterly = 4 times

Let's find the amount that must be deposited into the account quarterly.

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$FV=P(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})$

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Thus, we have:

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Let's solve for P.

We have:

$\begin{gathered} 28000=P(\frac{(1+0.01325)^{24}-1}{0.01325}) \\ \\ 28000=P(\frac{(1.01325)^{24}-1)^{}}{0.01325}) \\ \\ 28000=P(\frac{1.371509114-1}{0.01325}) \\ \\ 28000=P(\frac{0.371509114}{0.01325}) \end{gathered}$

Solving further:

$28000=P(28.0384237)$

Divide both sides by 28.0384237:

$\begin{gathered} \frac{28000}{28.0384237}=\frac{P(28.0384237)}{28.0384237} \\ \\ 998.6=P \\ \\ P=998.6 \end{gathered}$

Therefore, the amount that must be deposited quarterly into the account is $998.60

ANSWER:

$998.60

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