Q. 44.3( 16 Votes )

Find the values of a or b for which x = 3/4 or x = - 2 are the roots of the equation

ax2 + bx – 6 = 0

Answer :

Given x = 3/4 or x = - 2 are the roots of the equation

Putting in the equation gives -



;


9a + 12b-96 = 0


3a + 4b-32 = 0 - - - - - - - - - - - - - - - (1)


putting x = - 2 in equation gives



4a-2b-6 = 0


2a-b-3 = 0


2a-3 = b - - - - - - - - - - - (2)


Substituting (2) in (1)


3a + 4(2a-3)-32 = 0


11a-44 = 0


a = 4


b = 2(4)-3 = 5


Thus for a = 4 or b = 5; or x = - 2 are the roots of the equation


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