Question

Find the zeroes of a polynomial 16x2 - 25 and
verify relationship between the zeroes and the cofficients
$16x {}^{2} - 25$
​

Answer 1

Answer:

Zeroes are 0 and \frac{-1}{5}5−1

Step-by-step explanation:

Given: Quadratic Polynomial , 25x² + 5x

To find: Zeroes of Polynomial and Verify the relation between zeroes and coefficient

To find zeroes we equate polynomial with 0

⇒ 25x² + 5x = 0

5x ( 5x + 1 ) = 0

5x = 0  and 5x + 1 = 0

x = 0   and  x = \frac{-1}{5}5−1

Therefore, Zeroes are 0 and \frac{-1}{5}5−1

let, α = 0 and β = \frac{-1}{5}5−1

first relation is sum of zeroes/roots = \frac{-coefficient\:of\:x}{coefficient\:of\:x^2}coefficientofx2−coefficientofx

LHS = α + β = 0+\frac{-1}{5}=\frac{-1}{5}0+5−1=5−1

RHS = [tex\frac{-b}{a}=\frac{-5}{25}=\frac{-1}{5}[/tex]

LHS = RHS

Hence Verified

Second Relation is Product of zeroes/roots = \frac{constant\:term}{coefficient\:of\:x^2}coefficientofx2constantterm

LHS = αβ = 0\times]frac{-1}{5}=00×]frac−15=0

RHS = [tex\frac{c}{a}=\frac{0}{25}=0[/tex]

LHS = RHS

Hence Verified