Given the trinomial 2x*2 + 4x + 4, predict the type of solutions. a. Two rational solutions b. One rational solution c. Two irrational solutions d. Two complex solutions

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Given the trinomial 2x*2 + 4x + 4, predict the type of solutions. a. Two rational solutions b. One rational solution c. Two irrational solutions d. Two complex solutions

Mathematics
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The form of the roots of a quadratic expression is identified by the discriminant. The discriminant of the quadratic ax² + bx + c is: D = b² - 4ac If D ≥ 0, there are two real valued roots. If D = 0, there are two real, equal, rational which are sometimes erroneously interpreted as a single rational root. If D > 0 and is a perfect square, there are two real, unequal, and rational roots. If D > 0 and is not a perfect square, there are two real, unequal, and irrational roots. if D < 0, there are two complex valued solutions which form a complex conjugate pair. In this case, the quadratic is 2x² + 4x + 4, and the determinate is: D = 4² - 4(2)(4) = 16 -32 = -16 Since the determinate is less than zero, the form of the roots is a conjugate pair of complex roots or two complex roots

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2 complex solution. b^2 - 4ac >0
c:
d. Two complex solutions

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