Question

Find the quadratic polynomial the sum and product of those zero are -5 and 3 respectively

Answer 1

Given :

Sum of zeroes of Polynomial = -5

Product of zeroes of Polynomial = 3

$let \: the \: zeroes \: be \: \alpha \: and \: \beta$

We know that,

Quadratic equation :

=> f(x) = x² - (sum of zeroes)x + product of zeroes

$= > {x}^{2} - ( \alpha + \beta ) + ( \alpha \beta ) \\ \\ = > {x}^{2} - ( - 5)x + 3 \\ \\ = > {x}^{2} + 5x + 3$

Thus,the quadratic Polynomial is x² + 5x + 3.

Answer 2

Answer:

x² + 5x + 3

Step-by-step explanation:

Given Problem:

Find the quadratic polynomial the sum and product of those zero are -5 and 3 respectively.

Solution:

According to your question:

Sum of zeroes of Polynomial = -5  

Product of zeroes of Polynomial = 3

We know that,

x² - (sum of zeroes)x + product of zeroes.

Sum of zeroes = Alpha +Beta

Product of zeroes= Alpha.Beta

Alpha and Beta are two zeroes -3 and 2.

Now equation will be,

$\implies\ x^2 - (\alpha+\beta) + (\alpha.\beta)$

$\implies\ x^2 - (-5)x+3$

$\implies\ x^2 + 5x+3....................(Answer)$