Answer:
p = ±4√3
Step-by-step explanation:
The discriminant of quadratic equation ax²+bx+c = 0 is ...
d = b² -4ac
In your quadratic, its value is ...
d = p² -4(4)(3) = p² -48
The discriminant will be zero when the quadratic has equal roots. In that case, the values of p are found by ...
d = 0
p² -48 = 0
p² = 48 . . . . . add 48
p = ±√48 . . . . take the square root
p = ±4√3 . . . . simplify
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Another way to get there is by looking at the factoring of a quadratic with equal roots:
(ax +b)² = 0 = a²x² +2ab +b²
Comparing to the given quadratic, we find ...
a² = 4 ⇒ a = ±2 . . . . . . coefficient of x²
b² = 3 ⇒ b = ±√3 . . . . constant
p = 2ab = 2(±2)(±√3) . . . . coefficient of x
p = ±4√3
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The attachment shows the two different values of p give equations with one solution (each).
