Verify that i 4 is a zero of the polynomial- px - x - 4- ii -3 is a zero of the polynomial- q x - x - 3- iii 2-5 is a zero of the polynomial- fx - 2 - 5x-3 marks-

(i) p(x) = x 4 ⇒ p(4) = 4 4 = 0 Hence, 4 is the zero of the given polynomial. [1 nbsp;mark] (ii) q (x) = x + 3 ⇒ q( 3)= 3+3 ⇒ q( 3)=0 Hence, 3 is the zer ...

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Standard X

Mathematics

Zeros of a Polynomial

Verify that i...

Question

Verify that
(i) 4 is a zero of the polynomial, p(x) = x - 4.
(ii) -3 is a zero of the polynomial, q (x) = x + 3.
(iii) $\frac{2}{5}$ is a zero of the polynomial, $f (x) = 2 - 5 x$
[3 marks]

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Solution

(i) $p (x) = x - 4 \Rightarrow p (4) = 4 - 4 = 0$

Hence, 4 is the zero of the given polynomial.
[1 mark]

(ii) $q (x) = x + 3 \Rightarrow q (- 3) = - 3 + 3 \Rightarrow q (- 3) = 0$

Hence, 3 is the zero of the given polynomial.
[1 mark]

(iii) $f (x) = 2 - 5 x \Rightarrow f (\frac{2}{5}) = 2 - 5 \times \frac{2}{5} = 2 - 2 = 0$

Hence, $\frac{2}{5}$ is the zero of the given polynomial.
[1 mark]

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Similar questions

Verify that
(i) 4 is a zero of the polynomial, p(x) = x - 4.
(ii) -3 is a zero of the polynomial, q (x) = x + 3.
(iii) $\frac{2}{5}$ is a zero of the polynomial, $f (x) = 2 - 5 x$
(iv) $\frac{- 1}{2}$ is a zero of the polynomial, g(y) = 2y + 1.

Q. Verify that
(i) 1 and 2 are the zeros of the polynomial p(x) = x² − 3x + 2.
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Q. Verify that 2 is a zero of the polynomial x³ + 4x² − 3x − 18.

Q. Verify that
(i) 4 is a zero of the polynomial, p(x) = x - 4.
(ii) -3 is a zero of the polynomial, q (x) = x + 3.

Q. Verify whether the following are zeroes of the polynomial, indicated against them.
i)

p (x) = 3 x + 1, x = - \frac{1}{3}

ii)

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Verify that (i) 4 is a zero of the polynomial, p(x) = x - 4. (ii) -3 is a zero of the polynomial, q (x) = x + 3. (iii) 25 is a zero of the polynomial, f(x)=2−5x [3 marks]

(i) p(x)=x−4⇒p(4)=4−4=0 Hence, 4 is the zero of the given polynomial. [1 mark] (ii) q(x)=x+3⇒q(−3)=−3+3⇒q(−3)=0 Hence, 3 is the zero of the given polynomial. [1 mark] (iii) f(x)=2−5x⇒f(25)=2−5×25=2−2=0 Hence, 25 is the zero of the given polynomial. [1 mark]

Verify that
(i) 4 is a zero of the polynomial, p(x) = x - 4.
(ii) -3 is a zero of the polynomial, q (x) = x + 3.
(iii) $\frac{2}{5}$ is a zero of the polynomial, $f (x) = 2 - 5 x$
[3 marks]