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Georgia [21]
3 years ago
15

For what value of k is there one solution to the given quadratic equation (k+1)x²+4kx+2=0.

Mathematics
1 answer:
andriy [413]3 years ago
4 0

Answer:

If k = 1 or k = -\frac{1}{2}, there is only one solution to the given quadratic equation.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = (x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

The signal of \bigtriangleup determines how many real roots an equation has:

\bigtriangleup > 0: Two real and different solutions

\bigtriangleup = 0: One real solution

\bigtriangleup < 0: No real solutions

In this problem, we have the following second order polynomial:

(k+1)x^{2} + 4kx + 2 = 0.

This means that a = k+1; b = 4k; c = 2

It has one solution if

\bigtriangleup = 0

b^{2} - 4ac = 0

16k^{2} -8(k+1) = 0

16k^{2} - 8k - 8 = 0

We can simplify by 8

2k^{2} - k - 1 = 0

The solution is:

k = 1 or k = -\frac{1}{2}

So, if k = 1 or k = -\frac{1}{2}, there is only one solution to the given quadratic equation.

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Help please! Find the Surface area. Whoever gets it right ill give Brainliest!
11Alexandr11 [23.1K]

Answer:

284.6 square yards

284.6 yd^2

Step-by-step explanation:

Base: 7 × 13 = 91

Rectangle Sides: 6.1 × 13 = 79.3 (x2 = 158.6)

Triangle Sides: 5 × 7 = 35 (÷2 ×2 = 35)

Add: 91 + 158.6 + 35 = 284.6

8 0
3 years ago
Maria invested $450 in a savings account and earned $126 in interest at the end of 7 years.
Brut [27]
The interest rate is B. 4%

Given:
Principal = 450
Interest = 126
term = 7 
rate = ?

Simple Interest is computed by multiplying the Principal, rate, and term.

Interest = P × r × t

126 = 450 × r × 7
126 = 3150r
r = 126/3150
r = 0.04 x 100% = 4%

To check:

I = 450 
× 0.04 x 7
I = 18 × 7
I = 126
5 0
2 years ago
How do you do this?
Nat2105 [25]
U just need to add row by row
I'll do the first 1: 1+1=2
1+2=3
1+3=4
1+4=5
1+5=6
3 0
3 years ago
Read 2 more answers
Last week a sales representative earned a salary of $412.56 and a commission of 72.48 how much did the earn in all?
Lesechka [4]

Answer:

Step-by-step explanation:

He earned 485.04. You have to add. Hence the words in all

8 0
3 years ago
Pls help asap!! Hhuwdqnjwl
vampirchik [111]

Answer:

14

Step-by-step explanation:

To get the answer, add the whole numbers together and then add the fractions together:

9 + 4 = 13

(You can even stop here because 14 is the closest to 13)

Now, add the fractions:

\frac{2}{3}+\frac{1}{5}

To add fractions you have to have a common denominator. To find the common denominator multiply 3 by 5, and 5 by 3. Like this:

(\frac{5}{5})\frac{2}{3}  + \frac{1}{5} (\frac{3}{3} )

Simplify:

\frac{10}{15} +\frac{3}{15}              Distribute everything from above

\frac{13}{15}                      Add

So, the whole fraction will look like this 13\frac{13}{15}. This is closest to 14.

Hope this helps!! Ask questions if you need!

7 0
1 year ago
Read 2 more answers
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