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Zeroes of a Polynomial

Verify whethe...

Question

Verify whether the following are zeroes of the polynomial, indicated against them.
i) $p (x) = 3 x + 1, x = - \frac{1}{3}$
ii) $p (x) = 5 x - π, x = \frac{4}{5}$

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Solution

i)Given polynomial is $p (x) = 3 x + 1$

Therefore, zeros of the polynomial is $3 x + 1 = 0 ⟹ x = - \frac{1}{3}$

Hence, $x = - \frac{1}{3}$ is zero of the given polynomial.

ii)Given polynomial is $p (x) = 5 x - π$

Therefore, zeros of the polynomial is $5 x - π = 0 ⟹ x = \frac{π}{5}$

Hence, $x = \frac{4}{5}$ is not the zero of the given polynomial.

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Similar questions

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

(i) (ii)

(iii) p(x) = x² − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2

(v) p(x) = x², x = 0 (vi) p(x) = lx + m

(vii) (viii)

- \frac{1}{3}

p (x) = 5 x - π, x = \frac{4}{5}

p (x) = x^{2} - 1, x = 1, - 1

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

p (x) = i x + m, x = - \frac{m}{i}

p (x) = 3 x^{2} - 1, x = - \frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}

p (x) = 2 x + 1, x = \frac{1}{2}

p (x) = 5 x - 1; x = \frac{1}{5}

- \frac{1}{3}

p (x) = 5 x - π, x = \frac{4}{5}

p (x) = x^{2} - 1, x = 1, - 1

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

p (x) = i x + m, x = - \frac{m}{i}

p (x) = 3 x^{2} - 1, x = - \frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}

p (x) = 2 x + 1, x = \frac{1}{2}

p (x) = 3 x^{2} - 1, x = - \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}

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