Question

A
Complete the following activity to solve
the quadratic equation 9x + 6x = 4 by using quadratic formula.
Solution : 9x2 + 6x - 4 = 0 ..... General 1
;
c=
4
... comparing with general form
9 ; b = 6
Quadratic Formula,
-b+V
- 2a
... Formula
putting the values of a, b, c
2 x 9
simplifying
6 + L
18
... simplifying further
..
=
... by taking out common factor 6 and
cancelling with denominator​

Answer 1

Answer:

$x=\frac{-1+\sqrt{5} }{3}$ or $x=\frac{-1-\sqrt{5} }{3}$

Step-by-step explanation:

Question : Solve $9x^2+6x-4=0$ using quadratic formula.

$x=\frac{-b+\sqrt{b^2-4ac} }{2a}$ or $x=\frac{-b-\sqrt{b^2-4ac} }{2a}$

Put $b=2b'$.

Then, we get

$x=\frac{-b'+\sqrt{b'^2-ac} }{a}$ or $x=\frac{-b'-\sqrt{b'^2-ac} }{a}$.

And it's also a quadratic formula.

It's used when $b'$ is an integer.

$a=9, b'=3, c=-4$

$x=\frac{-3+\sqrt{9+36} }{9} =\frac{-3+\sqrt{45} }{9}=\frac{-1+\sqrt{5} }{3}$

or

$x=\frac{-3-\sqrt{9+36} }{9} =\frac{-3-\sqrt{45} }{9}=\frac{-1-\sqrt{5} }{3}$