Question

Factorize:
2x² + 3√5x + 5

Answer 1

Concept :  

Here we factorise it by splitting the middle term.

To factorise quadratic polynomials of the type ax² + bx + c by middle term splitting ,write b as the sum of two numbers whose product is ac.

To factorise ax² + bx - c & ax²- bx - c , write b as the difference of two numbers whose product is - ac.

 

 

Given : 2x² + 3√5x + 5

= 2x² +  2√5x + √5x + 5

= 2x (x + √5) +√5 (x + √5)

= (2x + √5) (x + √5)

Hence, the factorisation of 2x² + 3√5x + 5 is (2x + √5) (x + √5).

HOPE THIS ANSWER WILL HELP YOU…..

 

 Some questions of this chapter :

Factorize:

x²+5√5x+30

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Factorize:

X²+6√2x+10

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Answer 2

$\bf \huge{ \red{AnSwEr }:-}$

$\bf \orange{ = 2 {x}^{2} + 2 \sqrt{5}x + \sqrt{5} x + 5}$

$\bf \blue{ = 2x(x + \sqrt{5}) + \sqrt{5}(x + \sqrt{5} ) }$

$\bf \green{ = (x + \sqrt{5} (2x + \sqrt{5}) }$

$\bf \purple{∴2 {x}^{2} + 3 \sqrt{5}x + 5 = (x + \sqrt{5} (2x + \sqrt{5} }$