Question

3. The curve y= x^3-16x intersect x-axis at three points, then zeros of the curve are(a) 0,0,0. b)-4,4,4c) - 4,0,4. d)4,-4,4​

Answer 1

The zeros of the curve are - 4, 0, 4.

Step-by-step explanation:

The given curve is y = x³ - 16x and it intersects the x-axis at three points.

Therefore, there will be three values of x for y value equal to zero i.e. there are three zeros of the curve.

Now, putting y = 0, and solving the equation we get,

x³ - 16x = 0

⇒ x(x² - 16) = 0

⇒ x(x - 4)(x + 4) = 0

So, x = 0, 4 and -4.

Therefore, the zeros of the curve are - 4, 0, 4. (Answer)