We have given a quadratic polynomial f(x)=x²+x-2 and it is given that α and β are the zeroes of the given polynomial and we have to find the value of (1/α-1/β)
This is the basic and important question from polynomials as it was already asked in various examinations
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2C, question no 24
f(x)=x²−x−2
a=1
b=−1
c=−2
D=b²−4ac=(−1)²−4×1×(−2)=1+8=9
∵α and β are the zeroes of above polynomial.
∴ Sum of roots =−b/a
⇒α+β=−1/−1
⇒α+β=1⟶(1)
Difference of roots =√D/a
⇒∣β−α∣=√9/1=3
Product of roots =c/a
⇒αβ=−2/1
⇒αβ=−2⟶(2)
∴1/α−1/β=∣β−α∣/αβ
From eqn(1)&(2), we have
⇒1/α−1/β=3/−2=−3/2
Or
Simply find the roots of given equation & hence solve.