find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients​

2 thoughts on “find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients​”

1. 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:–

   • the standard quadratic Polynomial ax^2+bx+c
   • Sum of the zeroes = α +β= -b/a
   • Product of the zeroes = α β = c/a

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2. Answer:

   x2-sx +p

   x2+4x+3 is the quadratic polynomial

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