Question

Find the sum of the zeros of the polynomial 3x²-5
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Answer 1

$\huge{\red{\underline{Answer}}}$

$\boxed{\huge{0}}$

Solution:

To find the zeroes of the polynomial:

$\implies 3{x}^{2} - 5 \\ \implies 3{x}^{2} = 5 \\ \implies {x}^{2} = \frac{5}{3} \\ \implies x = \pm \sqrt{ \frac{5}{3} }$

Zeroes of polynomial $3x^{2} - 5$ are $-\sqrt{\dfrac{5}{3}}$ and $\sqrt{\dfrac{5}{3}}$

To find the sum of zeroes:

$\implies - \sqrt{ \frac{5}{3} } + \sqrt{ \frac{5}{3} } = 0$

Verification:

We know,

$\boxed{\frac{ - Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }}$

$= \frac{0}{3} \\ \\ = 0$

Hence, the sum of zeroes of polynomial $3x^{2} - 5$ is 0.

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☆ More to know ☆

Polynomial: It is an algebraic equation in which the degree of the polynomial is non-negative integral number and terms are arranged in ascending or descending order.

Sum of zeroes =

$\dfrac{-Coefficient \: of \: x}{Coefficient \:of \: x^{2}}$

Product of zeroes =

$\dfrac{Coefficient \: of \:constant}{Coefficient \:of \: x^{2}}$