For what values of the parameter a does the equation 2x ^ 2 + 4x + a = 0 have exactly one root?

| August 16, 2021 | education

For what values of the parameter a does the equation 2x ^ 2 + 4x + a = 0 have exactly one root? For the found value of the parameter a, indicate the corresponding root of the equation.

The quadratic equation 2x ^ 2 + 4x + a = 0 will have exactly one root when the discriminant of this quadratic equation is zero. Find the discriminant D of this quadratic equation:
D = 4 * 2 – 4 * 2 * a = 16 – 8 * a.
Let us find the values ​​of a for which the discriminant D is equal to zero. To do this, we solve the equation:
16 – 8 * a = 0;
8 * a = 16;
a = 16/8;
a = 2.
Therefore, the quadratic equation 2x ^ 2 + 4x + a = 0 will have exactly one root for a = 2. Find this root:
2x ^ 2 + 4x + 2 = 0;
x ^ 2 + 2x + 1 = 0;
(x + 1) ^ 2 = 0;
x + 1 = 0;
x = -1.

Answer: the equation 2x ^ 2 + 4x + a = 0 will have exactly one root for a = 2. The root of this equation for a = 2 is -1.



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