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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