Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial.
Answers
Step-by-step explanation:
Given :-
The zeroes are -2 and -5.
To find:-
Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial ?
Solution:-
Given zeroes are -2 and -5
Let α = -2 and β = -5
The quardratic polynomial whose zeores are α and β is K[x^2-(α+ β)x+αβ]
=>K[x^2-(-2-5)x+(-2)(-5)]
=> K[x^2-(-7)x+10]
=> K[x^2+7x+10]
If K = 1 then the required Polynomial x^2+7x+10
Relationship between the zeroes and the coefficients of x^2+7x+10:-
On Comparing this with the standard quadratic Polynomial ax^2+bx+c
a = 1
b= 7
c= 10
Sum of the zeroes
=α+ β
= -2-5
= -7
= -7/1
α+ β= -b/a
Product of the zeroes
= αβ
= (-2)(-5)
= 10
= 10/1
αβ= c/a
Verified the relationship between the zeroes and the coefficients of the given Polynomial.
Answer:-
The required Polynomial is x^2+7x+10
Used formulae:-
- The standard quadratic Polynomial ax^2+bx+c
- The quardratic polynomial whose zeores are α and β is K[x^2-(α+ β)x+αβ]
- Sum of the zeroes = -b/a
- Product of the zeroes = c/a