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Question
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
Solution
Given quadratic equations are
ax2 + x – 3a = 0 ...(i)
x2 + bx + b = 0 ...(ii)
Since, given x = –2 is the common solution of above quadratic equation.
∴ From equations (i),
a(–2)2 + (–2) – 3a = 0
⇒ 4a – 2 – 3a = 0
⇒ a = 2
From equation (ii),
(–2)2 + b(–2) + b = 0
⇒ 4 – 2b + b = 0
⇒ b = 4
Now, a2b = (2)2 × 4 = 4 × 4 = 16
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