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Radda [10]
3 years ago
9

The discriminant of the function is

Mathematics
1 answer:
inessss [21]3 years ago
6 0
Discriminant of a Quadratic

The number D = b2 – 4ac determined from the coefficients of the equation ax2 + bx + c = 0. The discriminant reveals what type of roots the equation has.

Note: b2 – 4ac comes from the quadratic formula.

 



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andrew-mc [135]
7 units. the side Mr is labeled as 3 units. and the side
4 0
3 years ago
Read 2 more answers
P(x)= 3x^3-5x^2-14x-4
nexus9112 [7]
   
\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\


\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)


\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm  \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm  \sqrt{4+16}}{2}=\frac{2\pm  \sqrt{20}}{2}=\frac{2\pm  2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}



7 0
3 years ago
Find the value of x for which 2x ^(1/ 2) = 32.
Mrac [35]

Answer:

The value of x will be 8    

Step-by-step explanation:

We have given that 2\sqrt{x}=32

We have to find the value of x

As 2\sqrt{x}=32

For finding the value of x we have to square both side

On squaring both side

We done squaring both side for easy simplification

4x=32

So x = 8

So the value of x will be 8

So answer will be 8

5 0
3 years ago
When should homeowners ask their lenders for mortgage modification
Fofino [41]

When they can no longer afford the mortgage but before they miss a payment.

5 0
3 years ago
6r + 7 = 13 + 7r what is r
kumpel [21]

Answer:

6r+7=13+7r

6r+7=7r+13

6r+7−7r=7r+13−7r

−r+7=13

−r+7−7=13−7

−r=6

\frac{-r}{-1} = \frac{6}{-1}

r=−6

Step-by-step explanation:

:) This is the answer

6 0
3 years ago
Read 2 more answers
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