1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fenix001 [56]
3 years ago
10

If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes

Mathematics
1 answer:
anyanavicka [17]3 years ago
5 0

ANSWER

x  =  2 \: \: or \:  \:  x  =  15

Or

x  =   - 2 \: \: or \:  \:  x  =   -  15

EXPLANATION

The given polynomial is

f(x) = {x}^{2}  + kx + 30

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

m + n =  -  \frac{b}{a}  =  -k

and the product of roots is

mn =  \frac{c}{a}  = 30

The square difference of the zeroes is given by the expression.

( {m - n})^{2} =  {(m + n)}^{2} - 4mn

From the question, this difference is 169.

This implies that:

( { - k)}^{2}  - 4(30) = 169

{  k}^{2}  -120= 169

k^{2} = 289

k=  \pm \sqrt{289}

k=  \pm17

We substitute the values of k into the equation and solve for x.

f(x) = {x}^{2}   \pm17x + 30

f(x) = (x  \pm2)(x  \pm 15)

The zeroes are given by;

(x  \pm2)(x  \pm 15) = 0

x  =  \pm2 \: \: or \:  \:  x  =  \pm 15

You might be interested in
Your bank statement indicates that you are overdrawn on your checking account by $250. How much must you deposit to bring the ch
andrey2020 [161]

Answer:

you would have to deposit $432.

Step-by-step explanation:

it's actually pretty simple. all you have to do is add 182+250 which equals 432. if you want to check your work, add 432 to -250 and you should get 182.

3 0
2 years ago
Solve each proportion. <br> 8/x+9=2/x-3<br> Please show work.
emmainna [20.7K]


8/x+9-(2/x-3)=0

Step by step solution :


Step 1 :

2
Simplify —
x
Equation at the end of step 1 :

8 2
(— + 9) - (— - 3) = 0
x x
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

3 3 • x
3 = — = —————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 - (3 • x) 2 - 3x
——————————— = ——————
x x
Equation at the end of step 2 :

8 (2 - 3x)
(— + 9) - ———————— = 0
x x
Step 3 :

8
Simplify —
x
Equation at the end of step 3 :

8 (2 - 3x)
(— + 9) - ———————— = 0
x x
Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x as the denominator :

9 9 • x
9 = — = —————
1 x
Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

8 + 9 • x 9x + 8
————————— = ——————
x x
Equation at the end of step 4 :

(9x + 8) (2 - 3x)
———————— - ———————— = 0
x x
Step 5 :

Adding fractions which have a common denominator :

5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(9x+8) - ((2-3x)) 12x + 6
————————————————— = ———————
x x
Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

12x + 6 = 6 • (2x + 1)

Equation at the end of step 6 :

6 • (2x + 1)
———————————— = 0
x
Step 7 :

When a fraction equals zero :

7.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

6•(2x+1)
———————— • x = 0 • x
x
Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
6 • (2x+1) = 0

Equations which are never true :

7.2 Solve : 6 = 0

This equation has no solution.
A a non-zero constant never equals zero.
7 0
3 years ago
Read 2 more answers
PLEASE HELP ME WITH 32D
mr_godi [17]

Answer:

Help me please in my question

4 0
2 years ago
Evaluate cot(-405°) I need help please
LuckyWell [14K]
x^\circ = x^\circ +360n
where n is a whole number

cot (\theta) = \frac{1}{tan(\theta)}
5 0
2 years ago
Read 2 more answers
Pregunta 14
IrinaK [193]

Answer:

sorry for points

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • A person stands 10 feet away from the base of a 300-foot office building.
    5·2 answers
  • Find the angles x and y in following figure.....correct answer will be mark BRAINLIEST and be followed...​
    10·1 answer
  • What is an expression for the calculation 2/3 times the sum of 2/8 and 4/8?
    13·1 answer
  • Into the boxes:<br> 2x + 8 = 1x + 9<br> Solve the equation.
    14·2 answers
  • Find the slope of the line through the points (-13,15), (20,-7)
    15·1 answer
  • Soumik has $5 less than his friend Kofi. If they have $97.50 altogether, how much does each
    6·2 answers
  • The equation y = 10x shows how the
    10·1 answer
  • Use the Remainder Theorem to determine whether or not x + 3 is a divisor of p (x) = 2x^3 + 4x^2 - 2x + 12
    14·2 answers
  • Can yoy please help solve yhis problem.2/5b+1=11​
    14·2 answers
  • Select all numbers that are solutions to the inequality w &lt; 1.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!