If lampa and beeta are the zeroes of a quadratic polynomial such that lampa +beeta =24 and lamps -beeta =8 find the quadratic polynomial having lamps and beeta as its zeroes verify the relationship between zeroes and coefficient of polynomial
Answers
polynomial eq. is x² - 24x + 128
Step-by-step explanation:
α + β = 24 ------------(1)
α - β = 8 -------------(2)
by using elimination method
on adding eq. 1 and 2
α + β = 24
α - β = 8
............................
2α = 32
α = 32/2
α = 16
put α in eq. 1
α + β = 24
16 + β = 24
β = 24 - 16
β = 8
now, polynomial eq is
x² - (α + β)x + αβ = 0
x² - (16+ 8)x + 16×8 = 0
x² - 24x +128 = 0
we know that ,
zeroes of polynomial is α and β
verification of zeroes
sum of zeroes = -b/a
16 + 8 = -(-24)/1
24 = 24
product of zeroes = c/a
16 × 8 = 128/1
128 = 128