Question

the sum and the product of the zeros of the quadratic polynomial are -1/2 and-3 respectivelywhat is the quadratic polynomial

Answer 1

Answer:

$2 {x}^{2} - x - 6$

p(x) = x^2 - Sx +P

Answer 2

The sum and the product of the zeros of the quadratic polynomial are -1/2 and-3 is x²+ $\frac{1}{2\\\\}$x - 3 = 0

Explanation:

If ax²+bx+ c = 0 is the quadratic equation.

Let the roots be x and y.

The sum of the roots, x + y = $\frac{-b}{a\\\\}$ ---- (1)

The product of the roots, xy = $\frac{c}{a\\\\}$ ---- (2)

Given:

x + y = $\frac{-1}{2\\\\}$

xy = -3

Substitute the values equation 1 and 2 .

$\frac{-1}{2\\\\}$ = $\frac{-b}{a\\\\}$ ⇒ $\frac{a}{2\\\\}$ = b

c = -3a.

Therefore, ax²+ $\frac{a}{2\\\\}$x - 3a = 0 ⇒ x²+ $\frac{1}{2\\\\}$x - 3 = 0

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