Beck Blake
04/06/2023 · Elementary School
5) Given the equation \( 4 x^{2}+8 x+k=0 \).. We sure to show wark is the discriminant? a) Folculator allowed, b) For what values of \( k \) will the equation have a repeated root? c) For what values of \( k \) will the equation have 2 real roots? d) For what values of \( k \) will the equation have imoginary roots? e) Name 3 values of \( k \) for which the given equation has rational roots. f) If \( (x+k)^{2}=x^{2}+22 x+k^{2} \) for all real numbers \( x \), then what does \( k \) equal? Explain your reasoning. f) 99
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a) Discriminant: \( D = 64 - 16k \)
b) Repeated root for \( k = 4 \)
c) 2 real roots for \( k < 4 \)
d) Imaginary roots for \( k > 4 \)
e) Rational roots for \( k = 4, 3, 0 \)
f) \( k = 11 \)
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