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3 years ago

4x^3+x^2-12x-3=0 factor by grouping

Mathematics

1 answer:

pentagon [3]3 years ago

7 0

(4x+1)(x^2-3)=0

x= -1/4 or +sqrt 3, -sqrt 3

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5. What is the value of x? х 4 in. 3 in. 6 in.

satela [25.4K]

Answer:

13in

Step-by-step explanation:

13in because if you add all

4 0

2 years ago

Find the discriminant and determine the nature of the roots to the quadratic equation

Katen [24]

№17
$x^{2} +6x-7=0 \\ D=6 ^{2} -4*(-7)=36+28=64=8 ^{2} \\ \\ x_{1} = \frac{-6+8}{2} =1 \\ \\ x_{2} = \frac{-6-8}{2} =-7$
Answer: x₁ = 1
   x₂ = - 7

№18
$2 x^{2} -3x+4=3 \\ 2 x^{2} -3x+4-3=0 \\ 2 x^{2} -3x+1=0 \\ \\ D= -3 ^{2} -4*2=9-8=1 \\ \\ x_{1} = \frac{3+1}{2*2} = \frac{4}{4} =1 \\ \\ x_{2} = \frac{3-1}{2*2} = \frac{2}{4} =0.5$
Answer: x₁ = 1
     x₂ = 0,5.

№19
$2 x^{2} -4x-5=0 \\ D=-4 ^{2} -4*2*(-5)=16+40=56 \\ \\ x_{1}= \frac{4+ \sqrt{56} }{2*2} = \frac{4}{4} + \sqrt{ \frac{56}{16} } =1+ \sqrt{3.5} \\ \\ x_{2} = \frac{4- \sqrt{56} }{2*2} = \frac{4}{4} - \sqrt{ \frac{56}{16} } =1- \sqrt{3.5} 
$
Answer: x₁ = 1 + √3.5
     x₂ = 1 - √3.5

3 0

4 years ago

Expand and Simplify (x-2)^2

Soloha48 [4]

Answer:

$\boxed{\ x^2-4x+4 \ }$

Step-by-step explanation:

$(x-2)^2 = (x-2)(x-2)=x(x-2)*-2(x-2)=x^2-2x-2x+4=x^2-4x+4$

3 0

3 years ago

Find all the integers,b, that make up the trinomial x2 + bx + 10 factorable.

KonstantinChe [14]

By the fundamental theorem of algebra, we can write

$x^2+bx+10=(x-r_1)(x-r_2)$

Expanding the right hand side, we get

$x^2+bx+10=x^2-(r_1+r_2)x+r_1r_2\implies\begin{cases}r_1+r_2=-b\\r_1r_2=10\end{cases}$

We want $b$ to be an integer, which means $r_1,r_2$ must also be integers. This means $r_1,r_2$ must be factors of 10. There are several possibilities:

$r_1=\pm10,r_2=\pm1\implies b=-(10+1)=-11\text{ or }b=-(-10-1)=11$

$r_1=\pm5,r_2=\pm2\implies b=-(5+2)=-7\text{ or }b=-(-5-2)=7$

So there are 4 possible values for $b$ : -11, -7, 7, and 11.

7 0

3 years ago

2x+3y = 15 x-3y=3 Solve

Arada [10]

By process of elimination. 3y and -3y get eliminated. Giving you

3x=18

Divide by 3 on each side

Giving you x=6

Plugging it into equation 2 you get

(6)-3y=3

Taking out the parenthesis you have

6-3y=3

Subtract by 6 on each side giving you

-3y=-3

Divide by -3 on each side giving you

y=1

So the answer for this equation is x=6 and y=1 or the ordered pair (6,1)

6 0

3 years ago