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Question: Let two numbers have A.M. = 9 & G.M. = 4. Then these numbers are roots of equation –...

Let two numbers have A.M. = 9 & G.M. = 4. Then these numbers are roots of equation –

A

x2 + 18x + 16 = 0

B

x2 – 18x + 16 – 0

C

x2 + 18 x – 16 = 0

D

x2 – 18x – 16 = 0

Answer

x2 – 18x + 16 – 0

Explanation

Solution

Let roots are a, b

A = α+β2\frac { \alpha + \beta } { 2 } ̃ a + b = 2A = 2 × 9 = 18

G = αβ\sqrt { \alpha \beta } ̃ ab = G2 ̃ ab = 42 = 16

quadratic eqn is x2 – Sx + P = 0

̃ x2 – 18 x + 16 = 0