Question

Find the roots of the quadratic polynomials:

6x−2x^2+8

a) x=−1,4
b) x=2,−4
c) x=1,−3
d) x=−2,3

Answer 1

The quadratic polynomial 6x - 2x² + 8 can be solved using the quadratic formula, resulting in the roots x = -1 and x = 4, which corresponds to option a) x = -1, 4.

Step-by-step explanation:

To find the roots of the quadratic polynomial 6x - 2x² + 8, we should first write it in standard form, which is ax² + bx + c = 0. For this equation, a = -2, b = 6, and c = 8.

Using the quadratic formula, x = (-b ± √b² - 4ac) / (2a), we can find the roots of the equation.

Substituting the values, we get:

x = ( -6 ± √(6² - 4(-2)(8)) ) / (2(-2))

x = ( -6 ± √(36 + 64)) / (-4)

x = ( -6 ± √100) / (-4)

x = ( -6 ± 10) / (-4)

There are two possible solutions for x:

• x = ( -6 - 10 ) / (-4) = -16 / -4 = 4
• x = ( -6 + 10 ) / (-4) = 4 / -4 = -1

Therefore, the roots of the polynomial are x = -1 and x = 4. (Option A)