Question

if alpha and beta are the roots of the equation x2-2x+3,then find the equation whose roots are (alpha+2) and (beta+2)​

Answer 1

Answer:    x² - 6x + 11 = 0,

Step-by-step explanation:      Hi,

Let α, β  be the roots of the equation

x² - 2x + 3 = 0,

Let f(x) = x² - 2x + 3

Given that roots are increased by 2, so new roots

of the equation are α + 2, β + 2

Let y = α + 2 which is the required root of new

equation,

So, α = y - 2

But, we know α is root of f(x), hence

f(α) = 0

But α = y - 2, so

f(y - 2) = 0

(y - 2)² - 2(y - 2) + 3 = 0

y² - 6y + 11 = 0,

Since similar argument holds for other root as

well, hence this equation represents the one

with roots α + 2 and β + 2

Changing the variable y to x, we get

x² - 6x + 11 = 0, which is the required equation.

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