Unknown: Welcome to R&H Academy
channel. Till yet, we have known
two methods to solve a quadratic
equation first is splitting the
middle term. Second is
completing the square method.
Today, we will learn third
method,
which is quadratic formula,
quadratic formula is x equals to
minus b plus minus root d by two
A, B is the coefficient of x,
A is the coefficient of x sq
whereas, D is b square
minus 4ac. D stands for
discriminant. And that's all you
need to know to solve question
number two, of Exercise 4.2
So,let's start. What is a? a is
the coefficient of x square, B
is coefficient of x that is
minus seven, C is constant.
Now, find out the D.
D is equal to b square minus
4AC, substitute the values B is
minus seven minus seven whole
square minus four, multiply a,
multiply three minus seven
square is 49. Minus four
multiply two multiply three is
24.
And 49 minus 24 is 25. Now, use
the formula x is equals to minus
b plus minus root d by 2a.
Substitute the values, B is
minus seven,
plus minus,
under root or square root of
twenty five by two
multiply two.
Let's simplify.
x is equal to
minus of minus seven is plus
seven, plus minus square root of
25 is five
divided by two multiply two is
four. So x equals to seven, plus
four minus five is equal to
four. x is equal to seven plus
five divided by four. x is
equals to seven minus 5 divided
by four, seven plus five is 12.
12 by four is three, seven minus
five is two by four and two by
four is one by three and one by
two are the values of x.
Step one
is to write the value of a,
which is coefficient of x
square. B is the cofficient of
x, that is one, C is constant,
that is minus four. Step two is
to find the value of
D or discriminant.
substitute these values
b square is one square, minus
four, multiply a that is two.
Multiply, c that is minus four.
One square is one,
minus four multiply two multiply
minus four is
plus 32.
And one plus 32 is 33. Use the
formula
x is equals to minus b
plus minus root d by two A
minus B is minus one,
plus minus root B is root 33
divided by two, multiply a, that
is four. So x is equals to minus
one
plus root 33 divided by two
multiply two is four. Another is
x equals to minus one minus root
33 divided by four. These are
the roots of given equation;
roots or solutions or the zeroes
of the given quadratic equation.
Let's move to part three
A,
B, and
C. A is coefficient of x square,
b is coefficient of x, C is
constant.
Find D,
D is equals to b square
minus four AC. B is four root
three whole square. minus four,
multiply a multiply C,
four root three square is
Four square, multiply root three
square, four square is 16. And
root three square is 3. 16
Multiply three is 48. 48 minus
four, 4 x 4 = 16. 16 into three
is 48. And 48 minus 48 is zero,
use the quadratic formula, x is
equals to minus b plus minus
root d by two A minus B is minus
four root three, plus minus b is
zero, square root of zero,
divided by two, multiply eight,
that is four minus four Three
plus minus
square root of zero is
zero divided by eight.
So x is minus 4 root 3 by eight,
plus zero will give
minus four root three by x is
equals to minus four
root three,
minus zero by 8. minus four root
three minus zero is minus four,
three, divided by eight.
Step one
is to write the values of A, B
and C. A is two B is one, C is
four,
D is equal to b square minus
4AC. b square is one square
minus four, multiply a, multiply
c, one square is
one minus four multiply
two multiply four is 32. And one
minus 32 is
minus 31.
Since D is less than zero, real
roots of the given quadratic
equation do not exist. So our D
should always be greater than or
equal to zero. For roots to
exist, else real roots do not
exist. Thank you so much for
watching.
