Algebra

for a quadratic to have a double root we want the variables of b^2 -4ac = 0

 

we can combine like terms in this quadratic via simplification and get 

 

x^2+11x+4x + k 

==> x^2 + 15x + k = 0

now we just plug this into the discriminant equation ( b^2 - 4ac = 0  ) 

== > 15^2 - 4 x 1 x c =0

simplfy == > 225 - 4c = 0 

thus c = 56.25

 

please check if this is right 

 

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.  

 

                                                                    2x² + 3x + 8x – x² + 4x + k   

 

combine like terms                                         x² + 15x + k   

 

for a quadratic to have a double root,   

which is also called a repeated root,   

its discriminant must equal zero

 

when a quadratic is in the form ax² + bx +c   

its discriminant is the quantity b² – 4ac            b² – 4ac   

                                                                       15² – (4)(1)(k)   

                                                                       225 – 4k    

 

solve for k                                                          k  =  (225 / 4)    

 

                                                                           k  =  56.25    

 

by the way, the quadratic in this problem factors to (x + 7.5)(x + 7.5)   

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