What should be subtracted from the polynomial x² − 16x + 30 so that 15 is the zero of the resulting polynomial?

Video Explanation

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Given

f(x) = x² − 16x + 30

To Find

The number which should be subtracted from f(x) so that 15 becomes a zero.

Solution

If 15 is a zero of the resulting polynomial, then:

f(15) − k = 0

where k is the number to be subtracted.

Step 1: Find f(15)

f(15) = (15)² − 16(15) + 30

= 225 − 240 + 30

= 15

Step 2: Find the Required Number

f(15) − k = 0

15 − k = 0

k = 15

Final Answer

The number that should be subtracted is:

15

Correct Option

(c) 15

Conclusion

Hence, 15 should be subtracted from the polynomial x² − 16x + 30 so that 15 is a zero of the resulting polynomial.