Answer: Consider the equation y=x3−x2+2x. y=x3−x2+2x. Whenever the graph passes through the X axis, the Y coordinate of the point of intersection would be 0. 0. ⇒ ⇒ The graph will cut the X axis whenever x3−x2+2x=0. x3−x2+2x=0. x3−x2+2x=0⇒x(x2−x+2)=0. x3−x2+2x=0⇒x(x2−x+2)=0. ⇒x=0 ⇒x=0 or x2−x+2=0. x2−x+2=0. The discriminant of x2−x+2=0 x2−x+2=0 is 1−8=−7<0. 1−8=−7<0. ⇒ ⇒ The equation x2−x+2=0 x2−x+2=0 does not have any real root. ⇒ ⇒ The equation x3−x2+2x=0 x3−x2+2x=0 has only one real root and it is x=0. x=0. When x=0,y=0. x=0,y=0. ⇒ ⇒ The graph of x3−x2+2x x3−x2+2x cuts the X axis only at one point. The coordinates of this point is (0,0). Step-by-step explanation: Mark me as BRAILNLIEST please Reply
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Answer:
Consider the equation y=x3−x2+2x. y=x3−x2+2x.
Whenever the graph passes through the X axis, the Y coordinate of the point of intersection would be 0. 0.
⇒ ⇒ The graph will cut the X axis whenever x3−x2+2x=0. x3−x2+2x=0.
x3−x2+2x=0⇒x(x2−x+2)=0. x3−x2+2x=0⇒x(x2−x+2)=0.
⇒x=0 ⇒x=0 or x2−x+2=0. x2−x+2=0.
The discriminant of x2−x+2=0 x2−x+2=0 is 1−8=−7<0. 1−8=−7<0.
⇒ ⇒ The equation x2−x+2=0 x2−x+2=0 does not have any real root.
⇒ ⇒ The equation x3−x2+2x=0 x3−x2+2x=0 has only one real root and it is x=0. x=0.
When x=0,y=0. x=0,y=0.
⇒ ⇒ The graph of x3−x2+2x x3−x2+2x cuts the X axis only at one point. The coordinates of this point is (0,0).
Step-by-step explanation:
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