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Svetlanka [38]
3 years ago
9

Use the quadratic formula to solve 9x2 + 6x – 17 = 0

Mathematics
1 answer:
USPshnik [31]3 years ago
3 0

The standard form of a quadratic equation is :

ax² + bx + c = 0

And the quadratic formula is:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.

So, first step is to compare the given equation with the above equation to get the value of a, b and c.

So, a = 9, b = 6 and c = - 17.

Next step is to plug in these values in the above formula. Therefore,

x=\frac{-6\pm\sqrt{6^2-4*(9)*(-17)}}{2*9}

=\frac{-6\pm\sqrt{36+612}}{18}

=\frac{-6\pm\sqrt{648}}{18}

=\frac{-6\pm\sqrt{324*2}}{18}

=\frac{-6\pm\sqrt{324}*\sqrt{2}}{18}

=\frac{-6\pm18*\sqrt{2}}{18}

=-\frac{6}{18} \pm\frac{18\sqrt{2}}{18}

=-\frac{1}{3} \pm\sqrt{2}.

So, x = -\frac{1}{3} \pm\sqrt{2}

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Finding a polynomial of a given degree with given zeros
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Since the real root is 4, then

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Since the complex root is (1 - i), then

The other root will be the conjugate of it (1 + i)

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x = (1 + i)

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x=4

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\begin{gathered} x-4=4-4 \\ x-4=0 \end{gathered}

The first factor is (x - 4)

\begin{gathered} x=1-i \\ x-(1-i)=(1-i)-(1-i) \\ x-1+i=0 \end{gathered}

The second factor is (x - 1 + i)

The third factor is (x - 1 - i)

f(x)=(x-4)(x-1+i)(x-1-i)

We will multiply them to find f(x)

\begin{gathered} (x-1+i)(x-1-i)= \\ x^2-x-ix-x+1+i+ix-i-(i^2)= \\ x^2-2x+1-(-1)= \\ x^2-2x+1+1= \\ x^2-2x+2 \end{gathered}

Multiply it by (x - 4)

\begin{gathered} f(x)=(x-4)(x^2-2x+2) \\ f(x)=x^3-2x^2+2x-4x^2+8x-8 \\ f(x)=x^3-6x^2+10x-8 \end{gathered}

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The number of children at the library was 3 times the number adults. The total number of people at the library was 48. How many
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Answer:

D 36

Step-by-step explanation:

<em>Write the information algebraically</em>

c = 3a

c + a = 48

c = children, a = adults

<em>In the second sentence (in bold), we can replace c with 3a</em>

c + a = 48 → 3a + a = 48

<em>Simplify</em>

3a + a = 48 → 4a = 48 → a = 12 (divide both sides by 4)

<em>We can then substitute or plug in a = 12 into the original equation:</em>

c + a = 48 → c + 12 = 48 → c = 36 (subtract 12 from both sides)

<h3>There are 36 children</h3>
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