Question

The equation formed by decreasing each root of ax? + bx + c = 0 by 1 is 2x² + 8x + 2 = 0 ​

Answer 1

Step-by-step explanation:

Let α and β be the roots of the original equation

∴ New roots ( α − 1 , β − 1 )

∴ α - 1 + β - 1 = $-\frac{8}{2}$

∴ α × β = −4 + 2

∴ α + β = −2                (1)

Also,

( α − 1 )( β − 1 )= α × β + 1 − α − β = 1

∴ α × β = α + β

∴ α × β = −2 = c          (2)

Now  $\frac{-b}{a} = \frac{c}{a}$

∴ b = -c

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By Abhiram5566

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