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Find the values of P for which the quadratic equation 4x²+px+3=0?

klasskru [66]

<h3><u>Correct Questions :- </u></h3>

Find the values of P for which the quadratic equation 4x²+px+3=0 , provided that roots are equal or discriminant is zero .

<h3><u>Solution</u>:- </h3>

Let us Consider a quadratic equation αx² + βx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

For equal roots

D = 0

$\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}}$

So,

$\sf{ β² - 4αc = 0}$

Here,

α = 4
β = p
c = 3

Now,

$\begin{gathered}\implies\quad \sf p²- 4 \times 4 \times 3 =0 \end{gathered}$

$\begin{gathered}\implies\quad \sf p²- 48 =0 \end{gathered}$

$\begin{gathered}\implies\quad \sf p²=48\end{gathered}$

$\begin{gathered}\implies\quad \sf p=±\sqrt{48}\end{gathered}$

$\begin{gathered}\implies\quad \sf p=±\sqrt{2 \times 2 \times 2 \times 2 \times 3} \end{gathered}$

$\begin{gathered}\implies\quad \sf p=± 2\times 2\sqrt{ 3 }\end{gathered}$

$\begin{gathered}\implies\quad \boxed{\sf{p=±4\sqrt{ 3 }}}\end{gathered}$

Thus, the values of P for which the quadratic equation 4x²+px+3=0 are-

4√3 and -4√3.

7 0

2 years ago

1 Marlena has a bag of coins. The bag

poizon [28]

Answer:

The probability is 1/6

Step-by-step explanation:

Firstly, we need to get the total number of coins

that would be the sum of all the coins present

We have this as;

8 + 10 + 4 + 2 = 24 coins

The number of nickels is 4

So the probability of selecting a nickel is the number of nickels divided by the total number of coins

We have this as;

4/24 = 1/6

8 0

3 years ago

Sylvia earns $7 per hour at her after school job. After working one week, she received a paycheck for $91.

makvit [3.9K]

Answer:

a.) $hours=13$

b.) $h\leq 15$

c.) $ $$105$

Step-by-step explanation:

a.) If she earns $7 'per' hour, this multiplication. After a week, we need to see how many hours she worked to earn $91, so this goes behind the equal sign. Let <em>h</em> be the unknown number of hours:

$7h=91$

Solve for h. Divide both sides by 7:

$\frac{7h}{7}=\frac{91}{7}\\\\h=13$

Sylvia worked 13 hours at a rate of $7 an hour.

b.) She can work at most 15 hours a week. At 'most' can also mean less than or equal to. Let <em>h</em> be hours:

$h\leq 15$

Sylvia can work less than or equal to 15 hours per week.

c.) If Sylvia can work 15 hours, plug in this value for <em>h</em> into an equation when she earns $7 per hour. Let the product of the hours and money equal <em>t</em> for total:

$t=7(15)\\t=105$

The most money Sylvia can earn in a week is $105.

<em>Finito.</em>

6 0

3 years ago

What is -3(2x-3)=-15

Oksanka [162]

Answer:

18

Step-by-step explanation:

-3(2x-3)

-3x(-6)

-3x-6=18 because the negatives cancel each other out.

7 0

3 years ago

Read 2 more answers

What is another name for <1?

Oksanka [162]

Option A:

The another name for ∠1 is ∠JLK.

Solution:

How to Label Angles :

There are two main ways to label angles:

1. Give the angle name by a number or a lower case letters.

2. The second way to name the angle is indicating by the vertex.

Usually the angle is denoted by three letters.

First letter and the second letter denotes the arms of the angle and the middle of the letter denotes the angle (its vertex).

To find the another name for ∠1.

The arms of the angle are LJ and LK and the vertex is L.

So, the name of the angle is ∠JLK.

Middle letter is the actual angle.

Therefore the another name for ∠1 is ∠JLK.

Option A is the correct answer.

8 0

3 years ago