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

ax^{2} + bx – 6 = 0

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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