Question

Find the quadratic polynomial where sum and product of zeros are 3 and (-1/2)​

Answer 1

Answer:

2$x^{2}$ + 6x -3 = 0

Step-by-step explanation:

Let zeros be α and β

sum of zeros (α+β) is 3

product of zeros (αβ) is  (-1/2)​

Quadratic equation is

    $x^{2}$ + (α+β) x +αβ = 0

   $x^{2}$ + 3x + (-1/2) = 0

   2$x^{2}$ + 6x -1 = 2

   2$x^{2}$ + 6x -3 = 0

Answer 2

Answer:

Given that

Sum of zeros = 3

and Product = -1/2

Now,

Using formula

f(x)= k{x2 - (sum of zeros) x + Product of zeros}

so,

f(x)= k{x2- (3)x+(-1/2)}

f(x)= k{x2- 3x - 1/2}

Answer is x2- 3x -1/2