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The equation of a curve is given as y=x^...

The equation of a curve is given as `y=x^(2)+2-3x`.
The curve intersects the x-axis at

A

(1,0)

B

(2,0)

C

Both (1) and (2)

D

No where

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To find the points where the curve intersects the x-axis, we need to set \( y = 0 \) in the equation of the curve. The equation given is: \[ y = x^2 + 2 - 3x \] ### Step 1: Set the equation to zero To find the x-intercepts, we set \( y \) to zero: \[ 0 = x^2 + 2 - 3x \] ### Step 2: Rearrange the equation Rearranging the equation gives us: \[ x^2 - 3x + 2 = 0 \] ### Step 3: Factor the quadratic equation Next, we will factor the quadratic equation. We need two numbers that multiply to \( 2 \) (the constant term) and add up to \( -3 \) (the coefficient of \( x \)). The numbers \( -1 \) and \( -2 \) satisfy these conditions: \[ (x - 1)(x - 2) = 0 \] ### Step 4: Solve for x Now, we can set each factor equal to zero: 1. \( x - 1 = 0 \) → \( x = 1 \) 2. \( x - 2 = 0 \) → \( x = 2 \) ### Conclusion The curve intersects the x-axis at the points \( x = 1 \) and \( x = 2 \). ### Final Answer The points of intersection are \( (1, 0) \) and \( (2, 0) \). ---
To find the points where the curve intersects the x-axis, we need to set \( y = 0 \) in the equation of the curve. The equation given is: \[ y = x^2 + 2 - 3x \] ### Step 1: Set the equation to zero To find the x-intercepts, we set \( y \) to zero: ...
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