Question

(5x - 3 + ✓5)×(5x - 3 - ✓3). Tell me the quadratic polynomial.

Answer 1

Hi Mate !!


Let's do it step by step :)
By Using Distributive law according to which :-

a ( b + c ) = ab + ac !!


(5x - 3 + ✓5)×(5x - 3 - ✓3)

5x ( 5x - 3 - √3 ) - 3 ( 5x - 3 - √3 ) +
√5 ( 5x - 3 - √3 )

=> 25x² - 15x - 5√3x - 15x + 9 + 3√3 + 5√5x - 3√5 - √15


Now collecting like terms ;

=> 25x² - 30x - 5√3x + 5√5x + 9 + 3√3 - 3√5 - √15

=> 25x² - ( 30 + 5√3 + 5√5 )x + 9 + 3√3 - 3√5 - √15

above is the required quadratic polynomial when ,
(5x - 3 + ✓5)×(5x - 3 - ✓3) is given !!

• [ I think the question is
(5x - 3 + ✓3 )×(5x - 3 - ✓3) if it is so then ]

Following the same rule !!

5x ( 5x - 3 - √3 ) - 3 ( 5x - 3 - √3 ) +
√3 ( 5x - 3 - √3 )


=> 25x² - 15x - 5√3x - 15x + 9 + 3√3 + 5√3x - 3√3 - 3

now , Solving like term ;


=> 25x² - 30x + 6 Is the required quadratic polynomial !!