Question Number 1 :For this equation x^2 – 3*x – 18 = 0 , answer the following questions : A. Find the roots using Quadratic Formula ! B. Use factorization to find the root of the equation ! C. Use completing the square to find the root of the equation !Answer Number 1 :The equation x^2 – 3*x – 18 = 0 is already in a*x^2+b*x+c=0 form.As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 1, b = -3, c = -18.1A. Find the roots using Quadratic Formula ! Remember the formula, x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) Since a = 1, b = -3 and c = -18, we just need to subtitute the value of a,b and c in the abc formula. Which produce x1 = (-(-3) + sqrt( (-3)^2 – 4 * (1)*(-18)))/(2*1) and x2 = (-(-3) – sqrt( (-3)^2 – 4 * (1)*(-18)))/(2*1) Which is the same as x1 = ( 3 + sqrt( 9+72))/(2) and x2 = ( 3 – sqrt( 9+72))/(2) Which make x1 = ( 3 + sqrt( 81))/(2) and x2 = ( 3 – sqrt( 81))/(2) We got x1 = ( 3 + 9 )/(2) and x2 = ( 3 – 9 )/(2) The answers are x1 = 6 and x2 = -31B. Use factorization to find the root of the equation ! x^2 – 3*x – 18 = 0 ( x – 6 ) * ( x + 3 ) = 0 So we got the answers as x1 = 6 and x2 = -31C. Use completing the square to find the root of the equation ! x^2 – 3*x – 18 = 0 ,divide both side with 1 So we get x^2 – 3*x – 18 = 0 , Which means that the coefficient of x is -3 We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -3/2 = -1.5 Which means we can turn the equation into x^2 – 3*x + 2.25 – 20.25 = 0 And it is the same with ( x – 1.5 )^2 – 20.25 = 0 Which is the same with (( x – 1.5 ) – 4.5 ) * (( x – 1.5 ) + 4.5 ) = 0 And it is the same with ( x – 1.5 – 4.5 ) * ( x – 1.5 + 4.5 ) = 0 Do the addition/subtraction, and we get ( x – 6 ) * ( x + 3 ) = 0 The answers are x1 = 6 and x2 = -3...
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