Question

If α and β are the zeroes of a
quadratic polynomialu x2+x-2
then find value of (1/α-1/β)
​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

f(x)=x 2 −x−2

a=1

b=−1

c=−2

D=b

2 −4ac=(−1) 2 −4×1×(−2)=1+8=9

∵α and β are the zeroes of above polynomial.

∴ Sum of roots = a−b⇒α+β=− 1−1

⇒α+β=1⟶(1)

Difference of roots = aD ⇒∣β−α∣= 19 =3

Product of roots = ac⇒αβ= 1 −2 ⇒αβ=−2⟶(2)

∴ α − b 1 = αβ∣β−α∣

From eq n (1)&(2), we have

⇒ α1 − β1 = −23 = − 23

Hence, (A) is the correct answer.