What should be subtracted from the polynomial x2 - 16x + 30 so that the resulting polynomial will have a root 15;

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Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 1)
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  1. 16
  2. 15
  3. 14
  4. 30

Answer (Detailed Solution Below)

Option 2 : 15
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Detailed Solution

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Concept 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.

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