Question

P(x) = √7 X²- 6x-
13√7​

Answer 1

Correct Question:

Factorise p(x) = √7x^2 - 6x - 13√7

Answer:

p(x) = (x+√7)(√7x-13)

Step-by-step explanation:

Given a quadratic polynomial such that,

$p(x) = \sqrt{7} {x}^{2} - 6x - 13 \sqrt{7}$

To factorise it.

We will follow the middle term splitting method.

Solving further, we will get,

$= > p(x) = \sqrt{7} {x}^{2} - 13x + 7x - 13 \sqrt{7} \\ \\ = > p(x) = \sqrt{7} {x}^{2} + 7x - 13x - 13 \sqrt{7} \\ \\ = > p(x) = \sqrt{7} x(x + \sqrt{7} ) - 13(x + \sqrt{7} ) \\ \\ = > p(x) = (x + \sqrt{7} )( \sqrt{7} x - 13)$

Hence, we get, p(x) = (x+√7)(√7x-13)

Answer 2

Given , P(x) = √7 x² - 6x  - 13√7

Now factorize the given polynomial using middle term splitting method.

⇒ √7 x² + 7 x - 13 x - 13√7

⇒ √7 x ( x + √7 ) - 13 ( x + √7 )

⇒ ( x + √7 ) ( √7 x - 13 )

P(x) = ( x + √7 ) ( √7 x - 13 )

So , x = -√7  &  x = 13/√7

$\bigstar$ More Info :

While solving quadratic equations ,

One must aware of middle term splitting method. i.e., factors of numbers

Eg : ( Given )

( 13√7 ) ( √7 ) , - 6

( 91 ) , -6

So ,When we multiply we need to get 91 and when we add we need to get -6 .

So that is - 13 , 7