C
CraftExam
medium difficulty5 min

Verification of given zeros

To verify whether a number is a zero of a polynomial, substitute that number into the polynomial and check whether the value becomes 0.

In one line: Substitute and test for zero.

Practice This Concept

Understand it

  • Verification is a simple but important exam skill.
  • If a number is claimed to be a zero, substitute it carefully into the polynomial.
  • If the result is 0, the claim is correct.
  • If the result is not 0, then the number is not a zero.
  • This method also helps students avoid blind guessing.

Example

For p(x)=x2-4x+3, p(1)=1-4+3=0, so 1 is a zero.

Formula and rule

A number a is a zero of p(x) if and only if p(a)=0.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1Check whether 2 is a zero of x2-5x+6.
  2. 2Substituting x=2 gives 4-10+6=0, so 2 is a zero.

Method you can reuse

  1. 1Replace x by the given number.
  2. 2Compute each term carefully.
  3. 3Add or subtract all terms.
  4. 4Conclude whether the result is 0 or not.

Visual tip

On a graph, the same check appears as the point where the curve meets the x-axis at x=a.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How do you check whether a number is a zero of a polynomial?

Think first, then show answer
Substitute the number into the polynomial and see whether the value becomes 0. If the result is 0, the number is a zero; otherwise it is not.

Common wrong answer

A common wrong answer is to stop after getting a non-zero part of the expression. Verification must use the full polynomial value.

Don't mix this up

Students often substitute only one part of the expression and forget to use the full polynomial. That gives a wrong check.

Exam tip

Always write the substitution step clearly. One small sign mistake can change the final answer.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Verify a given value as a zero, or show that a number is not a zero by direct substitution.
  1. 1

    Enough for 1 mark

    To verify whether a number is a zero of a polynomial, substitute that number into the polynomial and check whether the value becomes 0.

  2. 2

    Add for 2 marks

    Example: For p(x)=x2-4x+3, p(1)=1-4+3=0, so 1 is a zero.

  3. 3

    Add for 3 marks

    If a number is claimed to be a zero, substitute it carefully into the polynomial.

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