what are the x - intercepts of the function ( f(x)=-x^{2}-x + 2 )?\n( (-2,0) ) and ( (1,0) )\n( (2,0) ) and…

what are the x - intercepts of the function ( f(x)=-x^{2}-x + 2 )?\n( (-2,0) ) and ( (1,0) )\n( (2,0) ) and ( (1,0) )\n( (-2,0) ) and ( (-1,0) )\n( (0,-2) ) and ( (0,1) )

what are the x - intercepts of the function ( f(x)=-x^{2}-x + 2 )?\n( (-2,0) ) and ( (1,0) )\n( (2,0) ) and ( (1,0) )\n( (-2,0) ) and ( (-1,0) )\n( (0,-2) ) and ( (0,1) )

Answer

Explanation:

Step1: Find the x - intercepts

Set (f(x)=0), so (-x^{2}-x + 2=0). Multiply both sides by (-1) to get (x^{2}+x - 2=0).

Step2: Factor the quadratic equation

Factor (x^{2}+x - 2). We need two numbers that multiply to (-2) and add up to (1). The numbers are (2) and (-1). So (x^{2}+x - 2=(x + 2)(x - 1)=0).

Step3: Solve for x

Set each factor equal to zero:

  • (x+2 = 0) gives (x=-2).
  • (x - 1=0) gives (x = 1).

Answer:

A. ((-2,0)) and ((1,0))