WAEC Further Mathematics 2022 Objective — Question 36

Question 36 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2022 Objective paper, with the correct answer and a full explanation.

If α and β are the roots of x²+mx−n=0, where m and n are constants, form the equation whose roots are 1/α and 1/β.

A. mnx²−n²x−m=0
B. mx²−nx+1=0
C. nx²−mx+1=0
D. nx²−mx−1=0Correct

Explanation

α+β=−m, αβ=−n. Sum of new roots = (α+β)/αβ = m/n; product of new roots = 1/αβ = −1/n. The equation x²−(sum)x+product=0 becomes x²−(m/n)x−(1/n)=0, or nx²−mx−1=0.

Sign up free to unlock

Score tracking
Practice history
Saved questions
Progress dashboard
Personalized sessions
Weak-topic breakdown

…and/or go further with premium services and No Ads.

Create free account

More questions from Further Mathematics 2022 Objective More Further Mathematics past papers