## 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

Tofind:–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.

Relationshipbetweenthezeroesandthecoefficientsofx^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

Usedformulae:–Answer:x2-sx +p

x2+4x+3 is the quadratic polynomial