Question

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

Answer 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

Answer 2

Answer:

x2-sx +p

x2+4x+3 is the quadratic polynomial