What should be added to the polynomial x² − 5x + 4 so that 3 is the zero of the resulting polynomial?

Video Explanation

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Given

f(x) = x² − 5x + 4

To Find

The number which should be added to f(x) so that 3 becomes a zero.

Solution

If 3 is a zero of the resulting polynomial, then:

f(3) + k = 0

where k is the number to be added.

Step 1: Find f(3)

f(3) = 3² − 5(3) + 4

= 9 − 15 + 4

= −2

Step 2: Find the Required Number

f(3) + k = 0

−2 + k = 0

k = 2

Final Answer

The number that should be added is:

2

Correct Option

(b) 2

Conclusion

Hence, 2 should be added to the polynomial x² − 5x + 4 so that 3 is a zero of the resulting polynomial.