Final answer:
To find the value of a in the quadratic equation P(x) = ax² + 4x + 2 such that it has two real roots, we need to use the discriminant.
Step-by-step explanation:
To find the value of a in the quadratic equation P(x) = ax² + 4x + 2 such that it has two real roots, we need to use the discriminant. The discriminant is given by b² - 4ac. In this case, a = a, b = 4, and c = 2. For the equation to have two real roots, the discriminant must be greater than zero. So, we have:
4² - 4a(2) > 0
Simplifying further, we get: 16 - 8a > 0
Now, solving for a, we have:
16 > 8a
a < 2
Therefore, if a < 2, the quadratic equation P(x) = ax² + 4x + 2 will have two real roots.