Question

For Experts, Aces & Genius.
Roots of polynomial P(x)
$p(x) = {x}^{2} - \frac{10}{3} x + 1 = 0$

Answer 1

Hey friend here is your answer

To make it easy first let's take the LCM

We have ,

X^2-10/3X+1=0

3X^2-10X+3. =0
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3

We have the equation , 3X^2-10X+3=0

Using middle term splitting ,

We need sum -- -10
Product --9
Splitting factor --- ( -9,-1)

It become ,

3X^2-9X-X+3=0

3X(X-3) -1(X-3)=0

(3X-1). ( X-3)
Thus,

X=3. X = 1/3

These are the required zeroes


Hope it helps you ✌✌


Pls mark brainliest:-))

Answer 2

Hey Mate !

Here is your solution :

p( x ) = x² - ( 10/3 )x + 1 = 0

=> x² - ( 10/3 )x + 1 = 0

=> ( 3x² - 10x + 3 )/3 = 0

=> ( 3x² - 10x + 3 ) = 0 × 3

=> 3x² - 10x + 3 = 0

Splitting middle term ,

=> 3x² -9x - x + 3 = 0

=> 3x ( x - 3 ) -1 ( x - 3 ) = 0

By taking ( x- 3 ) as common,

=> ( x - 3 ) ( 3x - 1 ) = 0

=> ( x - 3 ) = 0 ÷ ( 3x - 1 )

=> x - 3 = 0

=> x = 3

Or

=> ( x - 3 ) ( 3x - 1 ) = 0

=> ( 3x - 1 ) = 0 ÷ ( x - 3 )

=> 3x - 1 = 0

=> 3x = 1

=> x = 1/3

Hence, roots are ( 1/3 ) and 3.

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Hope it helps !! ^_^