Question

quiz 3
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f(x) = -4x² + 10x - 8
what is the value of the discriminant of f?

how many distinct real number zeros does f have?

Explanation:

Step1: Recall discriminant formula

For a quadratic function \( f(x) = ax^2 + bx + c \), the discriminant \( D \) is given by \( D = b^2 - 4ac \). Here, \( a = -4 \), \( b = 10 \), \( c = -8 \).

Step2: Calculate discriminant

Substitute values into the formula: \( D = (10)^2 - 4\times(-4)\times(-8) \)
\( = 100 - 4\times32 \)
\( = 100 - 128 \)
\( = -28 \)

Step3: Determine number of real zeros

For a quadratic, if \( D > 0 \), 2 distinct real zeros; \( D = 0 \), 1 real zero; \( D < 0 \), 0 distinct real zeros. Since \( D = -28 < 0 \), number of distinct real zeros is 0.

Answer:

Discriminant value: \(-28\)
Number of distinct real zeros: \(0\)