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Chapter 10: Q8. (page 665)

How many times does the graph ofy=x2鈭�4x+10cross the x-axis?

Short Answer

Expert verified

The graph ofy=x2鈭�4x+10 will cross the x-axis2 times.

Step by step solution

01

Step 1. State the concept of ‘zeroes of polynomial’.

All the values of the variable in a given polynomial which makes the polynomial zero are called as the zeroes of polynomial.

These zeroes will give the number of times the graph crosses the x-axis.

02

Step 2. Calculate the number of zeroes of the given equation.

The equation y=x2鈭�4x+10is a quadratic equation and its degree is 2.

The number of zeroes of a polynomial is equal to the highest degree of the polynomial.

Therefore, the equation y=x2鈭�4x+10has two zeroes.

03

Step 3. State the conclusion.

Since the equationy=x2鈭�4x+10has two zeroes, it will cross x-axis twice.

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