Question

If one root of the equation 2x^2 -5x +k = 0 is double the other.Find k?

Answer 1

Here is your solution :

Given,

=> 2x² - 5x + k = 0

Let , α and ß be its zeroes.

A/Q,

=> α = 2ß

Zeroes = ß and 2ß.

In the quadratic equation 2x² - 5x + k.

Coefficient of x² ( a ) = 2

Coefficient of x ( b ) = -5

Constant term ( c ) = k

We know the relationship between zeroes and coefficients of a quadratic equation.

=> Sum of zeroes = - b / a

=> α + ß = -b / a

=> 2ß + ß = - ( -5 ) / 2

=> 3ß = 5 / 2

=> ß = 5 / ( 2 × 3 )

•°• ß = 5/6 --------- ( 1 )

And,

=> Product of zeroes = c/a

=> αß = k/2

=> ( 2ß )ß = k/2

=> 2ß² = k/2

Substitute the value of ( 1 ),

=> 2 ( 5/6 )² = k/2

=> 2( 25/36 ) = k/2

=> ( 25/18 ) = k/2

=> k = [ ( 25 × 2 ) / 18 ]

•°• k = ( 25 / 9 ).

Hope it helps !!

Answer 2

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