Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and coefficients. Only e), f), g) ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=\pm\sqrt{2}}}}$

$\green{\tt{\therefore{Value\:of\:x=0\:and\:5}}}$

$\green{\tt{\therefore{Value\:of\:x=\pm3}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} - 2 = 0 \\ \\ \tt: \implies {x}^{2} - 5x = 0 \\ \\ \tt: \implies {x}^{2} - 9 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies value \: of \: x = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\\tt: \implies {x}^{2} - 2 = 0 \\ \\ \tt: \implies {x}^{2} - { (\sqrt{2} })^{2} = 0 \\ \\ \tt: \implies (x + \sqrt{2} )(x - \sqrt{2} )= 0 \\ \\ \green{\tt: \implies x = \pm \sqrt{2} } \\ \\ \bold{Similarly : } \\ \tt: \implies {x}^{2} - 5x = 0 \\ \\ \tt: \implies x(x - 5) = 0 \\ \\ \green{\tt: \implies x = 0 \: and \: 5} \\ \\ \bold{Similarly : } \\ \tt: \implies {x}^{2} - 9 = 0 \\ \\ \tt: \implies {x}^{2} - {3}^{2} = 0 \\ \\ \tt: \implies (x + 3)(x - 3) = 0 \\ \\ \green{\tt: \implies x = \pm3}$

Answer 2

QueStI0N -

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and coefficients -

[ 1 ] $\sf{\bold{ x^2 - 2 }}$

[ 2 ] $\sf{\bold{ x^2 - 5x }}$

[ 3 ] $\sf{\bold{ x^2 - 9 }}$

S0LUTI0N -

Here, we have been provided the following list of polynomials .

We need to obtain the Zeroes of the Polynomials and verify the relationship between the Zeroes and the Coefficients ...

[ 1 ] $\sf{\bold{ x^2 - 2 }}$

Here , the given Polynomial is $\sf{\bold{F(x) = x^2 - 2 }}$

To obtain the zero of the above polynomial , we need to equate it to zero , i.e, find the value of x for which f(x) is equal to 0 .

So ,

$\sf{\bold{ x^2 - 2 = 0}} \\ \\ \sf{ x^2 - 2 + 2 = 0 + 2 } \\ \\ \sf{ x^2 = 2 } \\ \\ \sf{ x = + \sqrt{2} \: and \: - \sqrt{2} } \\ \\ \sf{ Hence \: the \: required \: Zeroes \: of \: the \: polynomial \: are \: - } \\ \\ \sf{ x = + \sqrt{2} \: and \: - \sqrt{2} }$

[ 2 ] $\sf{\bold{ x^2 - 5x }}$

Here , the given Polynomial is $\sf{\bold{F(x) = x^2 - 5x }}$

To obtain the zero of the above polynomial , we need to equate it to zero , i.e, find the value of x for which f(x) is equal to 0 .

So ,

$\sf{\bold{ x^2 - 5x = 0}} \\ \\ \sf{ x^2 - 5x + 5x = 0 + 5x } \\ \\ \sf{ x^2 = 5x } \\ \\ \sf{ x = 0 , and \: 5 } \\ \\ \sf{ Hence \: the \: required \: Zeroes \: of \: the \: polynomial \: are \: - } \\ \\ \sf{ x = 0, and \: 5 }$

[ 3 ] $\sf{\bold{ x^2 - 9 }}$

Here , the given Polynomial is $\sf{\bold{F(x) = x^2 - 2 }}$

To obtain the zero of the above polynomial , we need to equate it to zero , i.e, find the value of x for which f(x) is equal to 0 .

So ,

$\sf{\bold{ x^2 - 9 = 0}} \\ \\ \sf{ x^2 - 9 + 9 = 0 + 9 } \\ \\ \sf{ x^2 = 9 } \\ \\ \sf{ x = + \sqrt{9} \: and \: - \sqrt{9} } \\ \\ \sf{ x = 3 \: , \: -3 } \\ \\ \sf{ Hence \: the \: required \: Zeroes \: of \: the \: polynomial \: are \: - } \\ \\ \sf{ x = 3, \: and \: - 3 }$

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