Consider the quadratic equation −3x² + 5x − 2 = 0 . Which of the following statements are true? Select all that apply. O There are two complex roots. O There are two real roots. O The discriminant is zero. O The discriminant is positive. The discriminant is a positive, perfect square. O There is 1 real double root.

Classify the quadratic form below. Then make a change of variable, x= Py, that transforms the quadratic form into one with no cross-product terms. Write the new quadratic form. -x; - 3x - 5x3 - 5x - 2x, x2 + 2x,x3 + 2x,×4 + 4x3×4 Classify the given quadratic form. O A. Negative definite B. Indefinite C. Positive semidefinite 'D. Negative semidefinite O E. Positive definite The new quadratic form is y' Dy = (Simplify your answer.)

Justify why the CIRCLED answer is correct vs. What many people input as their answer. An electrical engineer who is calculating the impedance of a circuit needs to solve this equation. 4x2 8x -19 - What are the solutions to the equation? Type the answer in the form a + bi in the box below. Simplify your answer as much as possible, and leave any radicals in radical form. V15 2+iv15 1+ vs 2 Your answer

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