
Notice that if

, then

. Recall the definition of the derivative of a function

at a point

:

So the value of this limit is exactly the value of the derivative of

at

.
You have
<u>Question:</u>
Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0
<u>Answer:</u>
The number of real solutions for the equation
is zero
<u>Solution:</u>
For a Quadratic Equation of form :
---- eqn 1
The solution is
Now , the given Quadratic Equation is
---- eqn 2
On comparing Equation (1) and Equation(2), we get
a = 1 , b = 5 and c = 7
In
,
is called the discriminant of the quadratic equation
Its value determines the nature of roots
Now, here are the rules with discriminants:
1) D > 0; there are 2 real solutions in the equation
2) D = 0; there is 1 real solution in the equation
3) D < 0; there are no real solutions in the equation
Now let solve for given equation

Since -3 is less than 0, this means that there are 0 real solutions in this equation.
Answer:
so to get a third you divide it by 3
first convert it to fraction
so it is 26/3
so do 26/3 divided by 3
so we do keep switch flip
26/3*1/3
so answer is 26/9 or 2 8/9
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
10x+8=3x-6
subtract 10x-3x
7x+8= -6
subtract -6-8
7x=-14
divide 7 into -14
x = -2
Hope this helps!
There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19
<h3><u>
Solution:</u></h3>
Given that, There are two numbers whose sum is 64.
Let the number be a and b in which a is bigger.
Then, a + b = 64 ------ eqn (1)
The larger number subtracted from 4 times the smaller number gives 31.
4 x b – a = 31
4b – a = 31 ----- eqn (2)
We have to find the numbers.
So, from eqn (2)
a = 4b – 31
Subatitute a in (1)
4b – 31 + b = 64
On solving we get
5b = 64 + 31
5b = 95
b = 19
So, b = 19, then eqn 1
a + 19 = 64
On simplification,
a = 64 – 19
a = 45
Hence, the two numbers are 45 and 19