find the zeros of x^2-5x+4 find relationship between zeros and coefficients
Answers
Step-by-step explanation:
Given:-
The quadratic polynomial X^2-5X +4
To find:-
Find the zeroes of X^2-5X +4 and find the relationship between zeros and coefficients
Solution:-
Given quadratic polynomial is X^2-5X+4
=>X^2-X-4X + 4
=>X(X-1)-4(X-1)
=>(X-1)(X-4)
To get the zeroes we have to equate the given Polynomial to zero.
=>(X-1)X-4)=0
=>X-1 = 0 or X-4 = 0
=>X = 1 or X = 4
The value of X = 1 and 4
Zeroes of the given quadratic polynomial are 1 and 4
Relationship between the zeroes and the coefficients:-
Given quadratic polynomial= X^2-5X+4
On Comparing this with the standard quadratic Polynomial ax^2+bx+c
a = 1
b= -5
c = 4
and we have zeroes = 1 and 4
Let α = 1 and β = 4
1) Sum of the zeroes
= - Coefficient of X/ Coefficient of X^2
= α+β
=>α+β = 1+4
=>α+β = 5
Sum of the zeroes = -b/a
=>-(-5)/1
=>5/1
=>5
Sum of the zeroes = α+β = -b/a
and
2) Product of the zeroes =
=Constant term / Coefficient of X^2= αβ
=>αβ = 1×4
=>αβ = 4
Product of the zeroes = c/a
=>4/1
=>4
Product of the zeroes= αβ =c/a
Verified the given relations.
Answer:-
Zeroes of the given Polynomial are 1 and 4
Sum of the zeroes = -b/a = 5
Product of the zeroes = c/a = 4
Used formulae:-
- The standard form of a quadratic polynomial is ax^2+bx+c, where a≠0, a,b,c are real numbers and x is the variable .
- Sum of the zeroes =
- Coefficient of X/ Coefficient of X^2
= -b/a
- Product of the zeroes =
Constant term / Coefficient of X^2
= c/a