Question

find the quadratic polynomial, whose sum of zeros is -3 and product of zeros is 5​

Answer 1

Answer:

The answer is

${x }^{2} + 3x + 5$

I will tell you how the answer came

Step by Step Explanation :

There is a formula that ;

If we know the sum and product of the zeroes, Then the Quadratic Expression will be ;

${x}^{2} - (sum \: of \: z) + (product \: of \: z)$

Where, z = Zeroes.

We Know that ;

Sum of Zeroes = -3

Product of Zeroes = 5

Then the form will be ;

${x}^{2} - ( - 3)x + (5)$

${x}^{2} + 3x + 5$

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Answer 2

Answer:

Quadratic polynomial is x² +3x+5

Step-by-step explanation:

A polynomial of degree two is called Quadratic polynomial

Let α and β be the zeros of polynomial p(x)

p(x) = x² - (α+β)x+αβ

Above equation is the relationship between root of polynomials

Root of polynomials  are -3 and 5

Sum of zeros is -3

Sum of zeros is  α+β

α+β =-3

Product of zeros is 5​

Product of zeros is αβ

αβ =5

Substitute these values in the above equation

p(x) = x² - (α+β)x+αβ

p(x) = x² -(-3)x+5

p(x) = x² +3x+5

Quadratic polynomial is x² +3x+5