Question

Assertion : The graph y = f(x) is shown in figure, for the polynomial f(x) . The number of zeros of f(x) is 4. Reason : The number of zero of the polynomial f (x) is the number of point of which f (x) cuts or touches the axes. *
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Answer 1

Both assertion and reason are true and the reason is the correct explanation of the assertion.

We can calculate the number of zeroes of any polynomial but plotting its graph and checking that exactly how many times the function cuts or touches the x-axis. That is how you count several zeroes of any polynomial.

Here in the graph f(x) cuts the x-axis that is x'x exactly 4 times.

Therefore, the number of zeroes of f(x) is 4.

Answer 2

Both Assertion and Reason are correct, and Reason is the correct explanation of the Assertion.

Let us analyze both statements.

Assertion : The graph y = f(x) is shown in figure, for the polynomial f(x) . The number of zeros of f(x) is 4.

Reason: The number of zeroes of the polynomial f (x) is the number of points at which f (x) cuts or touches the axes.

• The graph given represents a function y = f(x).

What is the zero of an equation?

• The zeroes of an equation are any variables that will produce the answer 0 when substituted into the equation of a polynomial.

          In this case, a zero will be any variable that gives

                                               ⇒f(x) = 0

• Thus, graphically this relation is possible wherever f(x) cuts or touches the x-axis, i.e, the x-intercepts.
• At x-intercepts, the value of x=0 so they represent the real zeroes of the equation.
• Since the graph cuts the axis at 4 points, hence there are 4 real zeroes of the equation.

Therefore, Both Assertion and Reason are correct, and Reason is the correct explanation of the Assertion.