If alpha and beta are the zeroes of the qudritic polynomial x²-5x+4 find the value of[tex] \frac{1}{ \alpha } + \frac{1}{ \beta } – 2 \alpha \beta [/tex] About the author Katherine
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 Reply
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