Question

Do you think that quadratic formula is more appropriate in solving for
all types of quadratic equations​

Answer 1

Answer:

7 is the answer

Step-by-step explanation:

The quadratic formula helps you solve quadratic equations, and is probably one of the top five formulas in math.  We’re not big fans of you memorizing formulas, but this one is useful (and we think you should learn how to derive it as well as use it, but that’s for the second video!).

If you have a general quadratic equation like this:

ax^2+bx+c=0ax  

2

+bx+c=0a, x, squared, plus, b, x, plus, c, equals, 0

Then the formula will help you find the roots of a quadratic equation, i.e. the values of xxx where this equation is solved.

The quadratic formula

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}x=  

2a

−b±  

b  

2

−4ac

​  

 

​  

x, equals, start fraction, minus, b, plus minus, square root of, b, squared, minus, 4, a, c, end square root, divided by, 2, a, end fraction

It may look a little scary, but you’ll get used to it quickly!

Practice using the formula now.

Worked example

First we need to identify the values for a, b, and c (the coefficients). First step, make sure the equation is in the format from above, ax^2 + bx + c = 0ax  

2

+bx+c=0a, x, squared, plus, b, x, plus, c, equals, 0:

x^2+4x-21=0x  

2

+4x−21=0x, squared, plus, 4, x, minus, 21, equals, 0

aaa is the coefficient in front of x^2x  

2

x, squared, so here a = 1a=1a, equals, 1 (note that aaa can’t equal 000 -- the x^2x  

2

x, squared is what makes it a quadratic).

bbb is the coefficient in front of the xxx, so here b = 4b=4b, equals, 4.

ccc is the constant, or the term without any xxx next to it, so here c = -21c=−21c, equals, minus, 21.

Then we plug aaa, bbb, and ccc into the formula:

x=\dfrac{-4\pm\sqrt{16-4\cdot 1\cdot (-21)}}{2}x=  

2

−4±  

16−4⋅1⋅(−21)

​  

 

​  

x, equals, start fraction, minus, 4, plus minus, square root of, 16, minus, 4, dot, 1, dot, left parenthesis, minus, 21, right parenthesis, end square root, divided by, 2, end fraction

solving this looks like:

\begin{aligned} x&=\dfrac{-4\pm\sqrt{100}}{2} \\\\ &=\dfrac{-4\pm 10}{2} \\\\ &=-2\pm 5 \end{aligned}  

x

​  

 

=  

2

−4±  

100

​  

 

​  

 

=  

2

−4±10

​  

 

=−2±5

​  

 

Therefore x = 3x=3x, equals, 3 or x = -7x=−7x, equals, minus, 7.

Answer 2

The quadratic formula is very useful and more appropriate than squaring method.

1. Consider a quadratic ax^2 + b x + c= 0, the roots of the quadratic equation can be found by using the formula,

$\frac{-b +- \sqrt{b^2-4ac} }{2a}$.

 

• The above formula can be used in any case irrespective of the value of the discriminant, methods like squaring and factorization become difficult if the roots are irrational or imaginary.

• The discriminant of a quadratic equation is determined by using the formula$D = \sqrt{b^2-4ac}$.  

• If D> 0 the roots are real and distinct, If D<0 the roots are imaginary, If D=0 the roots are real and equal.

• There is no method to find irrational roots except using the formula, even if the roots are irrational, it is not possible to find them using the factorization method.
• Hence, using the formula is a convenient method to find the roots of a quadratic equation.

Therefore, the use of this formula is a convenient method for solving a quadratic equation.