The fourth method of solving a
quadratic equation is by using the
quadratic formula , a formula that will solve all quadratic equations. Although the quadratic formula works on any quadratic equation in standard form, it is easy to make errors in substituting the values into the formula. Pay close attention when substituting, and use parentheses when inserting a negative number.
We can derive the quadratic formula by
completing the square . We will assume that the leading coefficient is positive; if it is negative, we can multiply the equation by
and obtain a positive
a . Given
we will complete the square as follows:
First, move the constant term to the right side of the equal sign:
As we want the leading coefficient to equal 1, divide through by
a :
Then, find
of the middle term, and add
to both sides of the equal sign:
Next, write the left side as a perfect square. Find the common denominator of the right side and write it as a single fraction:
Now, use the square root property, which gives
Finally, add
to both sides of the equation and combine the terms on the right side. Thus,
The quadratic formula
Written in standard form,
any quadratic equation can be solved using the
quadratic formula :
where
a ,
b , and
c are real numbers and
Given a quadratic equation, solve it using the quadratic formula
Make sure the equation is in standard form:
Make note of the values of the coefficients and constant term,
and
Carefully substitute the values noted in step 2 into the equation. To avoid needless errors, use parentheses around each number input into the formula.
Calculate and solve.
Solve the quadratic equation using the quadratic formula
Solve the quadratic equation:
Identify the coefficients:
Then use the quadratic formula.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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