Question

If alpha and beta are the zeroes of the qudritic polynomial x²-5x+4 find the value of
$\frac{1}{ \alpha } + \frac{1}{ \beta } - 2 \alpha \beta$
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Answer 1

Answer:

f(x)=x2−2x+3 have zeroes α,β

⇒α+β=2

⇒α⋅β=3

Now polynomial having  α+2,β+2 as roots is

p(x)=x2−(α+2+β+2)x+(α+2)(β+2)

=x2−(α+β+4)x+αβ+2(α+β)+4

=x2−(2+4)x+3+2(2)+4

⇒x2−6x+11