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Question 13
If $$12x^2- ax + 7 = ax^2 + 9x + 3$$ has only one (repeated) solution, then the positive integral solution of a is:
Solution
Given, $$12x^2- ax + 7 = ax^2 + 9x + 3$$
$$(a-12)x^2 + (a+9)x-4 = 0$$
If $$ax^2+bx+c=0$$ has equal roots, then $$b^2 = 4ac$$
$$(a+9)^2 = 4(a-12)(-4)$$
$$a^2+81+18a = 192-16a$$
$$a^2+34a-111 = 0$$
On solving above equation, we get a = 3 and a = -37.
Here, The positive integral solution will be 3.
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