Question
Download Solution PDFWhat should be subtracted from the polynomial x2 - 16x + 30 so that the resulting polynomial will have a root 15;
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept Used:
If any polynomial p(x) has a root x = a, then p(a) = 0.
Explanation:
We have the polynomial x2 - 16x + 30
Let c be the value which needed to be subtracted from the polynomial.
⇒ x2 - 16x + 30 - c has a root of 15.
If a polynomial has a root at x = 15, it means that when you substitute x = 15 into the polynomial, the result should be equal to zero.
⇒ 152 - 16 ⋅ 15 + 30 - c = 0
⇒ 225 - 240 + 30 - c = 0
⇒ 15 - c = 0
⇒ c = 15
So, you should subtract 15 from the polynomial x2 - 16x + 30 to make it have a root of 15.
Last updated on Jan 29, 2025
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