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If one root of the equation Ax2 + Bx + C = 0 is two and a half times the other, then which of the following is TRUE?
- A7B2 = 3CA
- B7B2 = 4CA
- C7B2 = 36CA
- D10B2 = 49CA
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CCommunity
Ax2 + Bx + C = 0
Let one root be P and then the other root will be 2.5P
⇒ P + 2.5P = -B/A (Sum of Roots)
⇒ 3.5P = -B/A ---- (1)
⇒ P × 2.5P = C/A (Product of Roots)
⇒ 2.5 P2 = C/A ---- (2)
From equation 1 and 2
⇒ 2.5 × B2/ (3.5 × 3.5 × A2) = C/A
⇒ B2 = 4.9AC
∴ 10B2 = 49AC
Let one root be P and then the other root will be 2.5P
⇒ P + 2.5P = -B/A (Sum of Roots)
⇒ 3.5P = -B/A ---- (1)
⇒ P × 2.5P = C/A (Product of Roots)
⇒ 2.5 P2 = C/A ---- (2)
From equation 1 and 2
⇒ 2.5 × B2/ (3.5 × 3.5 × A2) = C/A
⇒ B2 = 4.9AC
∴ 10B2 = 49AC