Find the Roots (Zeros) -5k^2-k+5=9

Problem

−5*k2−k+5=9

Solution

1. Rearrange the equation into standard quadratic form a*k2+b*k+c=0 by subtracting 9 from both sides.

−5*k2−k+5−9=0

−5*k2−k−4=0

2. Multiply the entire equation by −1 to simplify the coefficients.

5*k2+k+4=0

3. Identify the coefficients for the quadratic formula k=(−b±√(,b2−4*a*c))/(2*a)

a=5

b=1

c=4

4. Calculate the discriminant D=b2−4*a*c to determine the nature of the roots.

D=1−4*(5)*(4)

D=1−80

D=−79

5. Apply the quadratic formula using the imaginary unit i=√(,−1) since the discriminant is negative.

k=(−1±√(,−79))/(2*(5))

k=(−1±i√(,79))/10

6. Separate the expression into its real and imaginary parts.

k=−1/10±(i√(,79))/10

Final Answer

−5*k2−k+5=9⇒k=−1/10±(i√(,79))/10

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