Question

Draw the graph of y=x²-x^3. and find Zeroes​

Answer 1

Answer:

Draw the graphs of

y=x

2

−x−6

and find the zeroes in each case.

Medium

Solution

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y=x

2

−x−6

When x=−3

y=−3

2

−(−3)−6=9+3−6=6

When x=−2

y=−2

2

−(−2)−6=4−2−6=0

When x=−1

y=−1

2

−(−1)−6=1+1−6=−4

When x=0

y=0

2

−0−6=6

When x=1

y=1

2

−1−6=−6

When x=2

y=2

2

−2−6=4−8=−4

When x=3

y=3

2

−3−6=9−9=0

List of x and y

x −3 −2−101 23

y60 −4 −6−6−40

(x,y)=(−3,6),(−2,0),((−1,−4),(0,−6),(1,−6),(2,−4).(3,0)

∴The graph y=x

2

−x−6cuts X−axis at the points 3 and −2

∴ The zeroes of quadratic polynomial are −2 and 3.

Step-by-step explanation:

Clearly graph of y=x

2

−x−6 cut the x-axis at x=−2,3.

⇒x=−2,3 are zeros of y=x

2

−x−6.

Justification:

when x=−2;y=4+2−6=0

when x=3;y=9−3−6=0