Chapter 10: Q8. (page 665)

How many times does the graph of $y = x^{2} - 4 x + 10$ cross the $x$ -axis?

Short Answer

Expert verified

The graph of $y = x^{2} - 4 x + 10$ will cross the $x$ -axis2 times.

Step by step solution

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.

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

The equation $y = x^{2} - 4 x + 10$ is 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 $y = x^{2} - 4 x + 10$ has two zeroes.

Step 3. State the conclusion.

Since the equation $y = x^{2} - 4 x + 10$ has two zeroes, it will cross x-axis twice.

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How many times does the graph of $y = x^{2} - 4 x + 10$ cross the $x$ -axis?

Short Answer

Step by step solution

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

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

Step 3. State the conclusion.

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

Short Answer

Step by step solution

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

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

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

How many times does the graph of $y = x^{2} - 4 x + 10$ cross the $x$ -axis?