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How do you find the discriminant and how many and what type of solutions does #f(t) = 4t^2 - 3t +3# have?

Answer 1

Avery Alexander

#D = b^2 - 4ac# = 9 - 48 = - 39 < 0. This equation has 2 complex roots.

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Answer 2

Julia Adams

To find the discriminant of a quadratic equation in the form ( f(t) = at^2 + bt + c ), where ( a ), ( b ), and ( c ) are constants, the discriminant is given by ( \Delta = b^2 - 4ac ).

For the equation ( f(t) = 4t^2 - 3t + 3 ), ( a = 4 ), ( b = -3 ), and ( c = 3 ).

Plugging these values into the discriminant formula, we get: [ \Delta = (-3)^2 - 4(4)(3) = 9 - 48 = -39 ]

Since the discriminant is negative (( \Delta < 0 )), the quadratic equation ( f(t) = 4t^2 - 3t + 3 ) has two complex solutions.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.