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Zeroes of a Polynomial

p5 = 5 then, ...

Question

$p (5) = 5$ then, which polynomial from the following, it corresponds to?

p (x) = x^{2} - 5 x + 5

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p (x) = x^{2} - 5 x

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p (x) = x^{2} - x + 5

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p (x) = x^{2}

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Solution

The correct option is A $p (x) = x^{2} - 5 x + 5$
Let $p (x) = x^{2} - 5 x + 5$ and substitute $x = 5$ as shown below:

$p (5) = (5)^{2} - (5 \times 5) + 5 = 25 - 25 + 5 = 5$

Hence, $p (x) = x^{2} - 5 x + 5$ .

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p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

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(x + 3)

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Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x)=3x+1,x= $\frac{- 1}{3}$

(ii) p(x)=5x− $π$ ,x= $\frac{4}{5}$

(iii) p(x)= $x^{2}$ -1,x=1,−1

(iv) p(x)=(x+1)(x−2),x=−1,2

(v) p(x)= $x^{2}$ ,x=0

P (x) + q (x) = x^{2} - 4 x + 1 a n d P (x) - q (x) = x^{2} + 5 x - 2

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