Question

9x²+2x+1/9 factorise​

Answer 1

Answer:

Step-by-step explanation:

A whole number that is the square of an integer. Example:  

16

is a perfect square because  

4

⋅

4

=

16

.

Answer 2

Question -:-

Factorise

${\Large{\bf{ \implies9x^{2} + 2x + \cfrac{1}{9}}}}$

Answer -:-

We know that quadratic equation is in form of

• ax²+ bx + c

Also, We know about root of the quadratic equation can also be given by Quadratic formula.

${\large{\underline{\boxed{ \bf{\implies \frac{ - b \pm \sqrt{ {(b)}^{2} - 4ac } }{2a} }}}}}$

So,

${\large{\sf{\implies 9 {x}^{2} + 2x + \cfrac{1}{9} }}}$

Here

• a = 9
• b = 2
• c = 1/9

So, according to the question roots of the equation are :-

● 1st Value of x

$\bf{\implies \cfrac{ - b + \sqrt{ {(b)}^{2} - 4ac } }{2a} }$

$\bf{\implies \cfrac{ - 2 + \sqrt{ {(2)}^{2} - 4(9) \bigg( \cfrac{1}{9} \bigg) } }{18} }$

$\bf{\implies \cfrac{ - 2 + \sqrt{ 4 - \bigg( \cfrac{36}{9} \bigg) } }{18} }$

$\bf{\implies \cfrac{ - 2 + \sqrt{4 -4 } }{18} }$

$\bf{\implies \cfrac{ - 2 + \sqrt{0 } }{18} }$

$\bf{\implies \cfrac{ - 2 + 0 }{18} }$

$\bf{\implies \cfrac{ - 2 }{18} }$

${ \underline{ \boxed{ \green{\bf{\implies - \frac {1}{9} }}}}}$

■ Second value of x

$\bf{\implies \cfrac{ - b - \sqrt{ {(b)}^{2} - 4ac } }{2a} }$

$\bf{\implies \cfrac{ - 2 - \sqrt{ {(2)}^{2} - 4(9) \bigg( \cfrac{1}{9} \bigg) } }{18} }$

$\bf{\implies \cfrac{ - 2 - \sqrt{ 4 - \bigg( \cfrac{36}{9} \bigg) } }{18} }$

$\bf{\implies \cfrac{ - 2 - \sqrt{4 -4 } }{18} }$

$\bf{\implies \cfrac{ - 2 - \sqrt{0 } }{18} }$

$\bf{\implies \cfrac{ - 2 - 0 }{18} }$

$\bf{\implies \cfrac{ - 2 }{18} }$

${ \underline{ \boxed{ \green{\bf{\implies - \frac {1}{9} }}}}}$

So, roots of the equation are :-

${ \underline{ \boxed{ \green{\bf{\implies - \frac {1}{9} }}}}} \: \: \: \: \: \: \: { \underline{ \boxed{ \green{\bf{\implies - \frac {1}{9} }}}}}$