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3 years ago

What value of c makes x2 − 24x + c a perfect square trinomial? −144 −48 48 144

Mathematics

1 answer:

attashe74 [19]3 years ago

8 0

Answer:

144

Step-by-step explanation:

Hello, please consider the following.

$x^2-24x+c$

is a perfect square means that the discriminant is 0.

$\Delta = b^2-4ac=24^2-4c=0\\\\24^2-4c =0 4c=576\\\\\text{We divide by 4}\\\\c= \dfrac{576}{4}=144$

Thank you

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X = amount of the 18% solution

y = amount of the 40% solution

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likewise, how many liters are there in the 40% solution? well, (40/100) * y, or 0.4y, that many.

we know the mixture has to yield 10 liters at 20% alcohol, how many liters of only alcohol is that? well, (20/100) * 10, or 2 liters.

$\bf \begin{array}{lccclll}
&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\
&------&------&------\\
\textit{18\% solution}&x&0.18&0.18x\\
\textit{40\% solution}&y&0.40&0.4y\\
------&------&------&------\\
mixture&10&0.20&2
\end{array}$

$\bf \begin{cases}
x+y=10\implies \boxed{y}=10-x\\
0.18x+0.4y=2\\
----------\\
0.18x+0.4\left( \boxed{10-x} \right)=2
\end{cases}
\\\\\\
0.18x-0.4x+4=2\implies -0.22x=-2
\\\\\\
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Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading co

oksano4ka [1.4K]

f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.

<h3>Find the required equation:</h3>

The zeroes or roots of a polynomial function are x values for which f(x) = 0

If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is

⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)

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Here in the question it is given that,

Polynomial should be with degree 3
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By using the formula of polynomial function we get,

⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)

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