1.

A and b are the zeros of 4x^2-5x-1,then a^2b-b^2a=​

Answer»

Answer:

- √41 / 16

Step-by-step EXPLANATION:

Given-----> a and b are zeroes of ( 4x² - 5x - 1 )

To find -----> Value of ( a²b - b²a )

Solution-----> ATQ,

4x² - 5x - 1 has zeroes as a and b ,

We know that,

Sum of zeroes

= - Coefficient of x / Coefficient of x²

=> a + b = - ( - 5 ) / 4

=> a + b = 5 / 4

Product of zeroes

= Constant term / Coefficient of x²

AB = - 1 / 4

Now,

a²b - b²a = ab ( a - b )

= ab √( a - b )²

We know that,

( a - b )² = ( a + b )² - 4ab , putting it , we get

a²b - b²a = ab √{ ( a + b )² - 4ab }

= ( -1/4 ) √{ ( 5/4 )² - 4 ( -1/4 ) }

= ( -1/4 ) √{ ( 25/16) + 1 }

= ( -1/4 ) √{ ( 25 + 16) / 16 }

= ( -1/4 ) √( 41/16)

= ( -1/4 ) √41/ 4

= - √41 /16


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