Mathematics
If 3 and -3 are the solutions of equation ax2 + bx - 9 = 0; find the values of a and b.
Answer
Since, 3 is a solution of ax2 + bx - 9 = 0,
Substituting 3 in ax2 + bx - 9 = 0.
⇒ a(3)2 + b(3) - 9 = 0
⇒ 9a + 3b - 9 = 0
⇒ 9a + 3b = 9
⇒ 3(3a + b) = 9
⇒ 3a + b = 3 …….(i)
Since, -3 is a solution of ax2 + bx - 9 = 0,
Substituting -3 in ax2 + bx - 9 = 0.
⇒ a(-3)2 + b(-3) - 9 = 0
⇒ 9a - 3b - 9 = 0
⇒ 3(3a - b - 3) = 0
⇒ 3a - b - 3 = 0
⇒ b = 3a - 3 …….(ii)
Substituting value of b from (ii) in (i) we get,
⇒ 3a + 3a - 3 = 3
⇒ 6a = 6
⇒ a = 1.
Substituting value of a in (ii) we get,
⇒ b = 3(1) - 3
⇒ b = 3 - 3 = 0.
Hence, a = 1 and b = 0.
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