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3 years ago

If the discriminant of a quadratic equation is -4, how many solutions does the equation have?

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

5 0

No real solutions....................

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brilliants [131]

Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

4 0

3 years ago

colored markers cost 78 cents each Pablo has 21.62 dollars in his pocket how many markers can Pablo buy

USPshnik [31]

Answer:

he can buy 30

Step-by-step explanation:

21.62 divided by .78 = 30.0277777778,you dont have enough for 31

6 0

3 years ago

The distribution of individual incomes in the United States is strongly skewed to the right. In 2013, the mean and median income

vesna_86 [32]

Answer:

The mean would be $322,343 and the median would be $196,723.

Step-by-step explanation:

Since the distribution of individual incomes is skewed to the right, it means that the distribution has a long right tail.

Drawing a distribution with this characteristic, we can see how the majority of the data falls into the left side of the graphic, meaning that a lot of people receive less income. Following this reasoning, the mean which is the amount of the data (in this case individual income) divided by the amount of people, would be the higher number, meaning that the few people who earn more money would influence in making this number higher.

Following this reasoning, the median (which is not influenced by this difference) would be the less high number.

5 0

4 years ago

Confidence in banks: A poll conducted in 2012 asked a random sample of 1268 adults in the United States how much confidence they

Katena32 [7]

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3 0

3 years ago

an obtuse triangle has the side as x-3 on the left and then the right says x then the bottom says x+6 can you find the perimeter

user100 [1]

Answer:

P = (x-3) + (x+6) + x

P = 3x+3

Step-by-step explanation:

To find the perimeter of a figure, you just need to add all sides together. First, you need to set up an equation that adds all sides together. Then, you would need to combine like terms (x+x+x=3x); -3+6=3. So you would take 3x and add 3, since 3 is positive.

Hope this helps!

7 0

3 years ago