please answer my question??
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Answer:
b² = ac
Step-by-step explanation:
(i) ax² + 2bx + c = 0
On comparing with ax² + bx + c = 0, we get
a = a, b = 2b, c = c
Given that the equation has real roots.
b² - 4ac ≥ 0
⇒ (2b)² - 4ac ≥ 0
⇒ 4b² - 4ac ≥ 0
⇒ b² - ac ≥ 0
⇒ b² ≥ ac
(ii) bx² - 2√acx + b² = 0
On comparing with ax² + bx + c = 0, we get
a = b, b = -2√ac, c = b
Given that the equation has real roots.
b² - 4ac ≥ 0
⇒ (-2√ac)² - 4(b)(b) ≥ 0
⇒ 4ac - 4b² ≥ 0
⇒ ac - b² ≥ 0
⇒ ac ≥ b²
From (i) & (ii), we get
b² = ac.
Hope it helps!
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