find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients
Question
find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients
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Mathematics
2 years
2021-06-22T06:38:29+00:00
2021-06-22T06:38:29+00:00 2 Answers
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Answers ( )
Step-by-step explanation:
Given :–
Zeros -4 and 3
To find :–
Find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients ?
Solution:–
Given zeroes are -4 and 3
Let α = -4
and Let β = 3
We know that
The Quadratic Polynomial whose zeroes α and β
is K[x^2-(α +β)x +α β]
On Substituting these values in the above formula
=> K[x^2-(-4+3)x+(-3)(4)]
=> K[x^2-(-1)x+(-12)]
=> K[x^2+x-12]
If K = 1 then the quardratic polynomial is x^2+x-12.
Relationship between the zeroes and the coefficients of x^2+x-12:–
Quadratic polynomial = x^2+x-12
On Comparing this with the standard quadratic Polynomial ax^2+bx+c
a = 1
b = 1
c=-12
And
α = -4
β = 3
i) Sum of the zeroes
=> α +β
=> -3+4
=> – 1
=> -1/1
=> -(coefficient of x)/Coefficient of x^2
=> -b/a
Verified the relation.
And
ii) Product of the zeroes
=>α β
=> (-4)(3)
=> -12
=> -12/1
=> Constant term/ Coefficient of x^2
=> c/a
Verified the relationship between the zeroes and the coefficients.
Answer:–
The quardratic polynomial is x^2+x-12
Used formulae:–
Answer:
x2-sx +p
x2+4x+3 is the quadratic polynomial