Given two functions ( f(x) = x^2 - 3x + 2 ) and ( g(x) = -x^2 + 5x - 6 ). Find the roots of the function ( h(x) = f(x) - g(x) ).

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Accepted Answer

Step:1 ：Step 1: First, we need to find the expression for ( h(x) = f(x) - g(x) ). This is done by subtracting the function ( g(x) ) from ( f(x) ). So, ( h(x) = (x^2 - 3x + 2) - (-x^2 + 5x - 6) ).Step:2 ：Step 2: Simplify ( h(x) ) to get ( h(x) = 2x^2 - 8x + 8 ).Step:3 ：Step 3: To find the roots of ( h(x) ), we need to solve the equation ( h(x) = 0 ), i.e., ( 2x^2 - 8x + 8 = 0 ).Step:4 ：Step 4: Divide every term by 2 to simplify the equation. We get ( x^2 - 4x + 4 = 0 ).Step:5 ：Step 5: This is a perfect square trinomial. So, ( (x-2)^2 = 0 ).Step:6 ：Step 6: Solve for ( x ) to get the roots of the equation.

Answer

Step: 1 ：Step 1: First, we need to find the expression for ( h(x) = f(x) - g(x) ). This is done by subtracting the function ( g(x) ) from ( f(x) ). So, ( h(x) = (x^2 - 3x + 2) - (-x^2 + 5x - 6) ).Step: 2 ：Step 2: Simplify ( h(x) ) to get ( h(x) = 2x^2 - 8x + 8 ).Step: 3 ：Step 3: To find the roots of ( h(x) ), we need to solve the equation ( h(x) = 0 ), i.e., ( 2x^2 - 8x + 8 = 0 ).Step: 4 ：Step 4: Divide every term by 2 to simplify the equation. We get ( x^2 - 4x + 4 = 0 ).Step: 5 ：Step 5: This is a perfect square trinomial. So, ( (x-2)^2 = 0 ).Step: 6 ：Step 6: Solve for ( x ) to get the roots of the equation.

Given two functions $f (x) = x^{2} - 3 x + 2$ and $g (x) = - x^{2} + 5 x - 6$ . Find the roots of the function $h (x) = f (x) - g (x)$ .

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Popular Problems

Given two functions f(x)=x2−3x+2 and g(x)=−x2+5x−6. Find the roots of the function h(x)=f(x)−g(x).

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Popular Problems

Given two functions $f (x) = x^{2} - 3 x + 2$ and $g (x) = - x^{2} + 5 x - 6$ . Find the roots of the function $h (x) = f (x) - g (x)$ .