Question

Write a quadratic polynomial, sum of whose zeros is 2 and product is -8.​

Answer 1

Answer:

Let S and P denotes respectively the sum and product of the zeros of a polynomial are \(2 \sqrt{3}\) and 2. Hence, the quadratic polynomial is \(g(x)=k\left(x^{2}-2 \sqrt{3} x+2\right)\)where k is any non-zero real number

Answer 2

Answer:

Polynomial is

x² - 2x - 8

Step-by-step explanation:

In the given question, sum=2 and product=-8

So, let's take 4 and (-2) as the zeroes

LET'S PROVE THEY'RE THE ZEROES

sum= 4+(-2) = 4-2 =2

product= 4×(-2)= -8

So here we got the sum and product as given in the question.

Hence proved that 4 and -2 are the zeroes

Formula for writing a polynomial:

x² - (sum)x + (product)

Therefore the polynomial is

x² - 2x +(-8)

=> x² - 2x - 8

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