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Home » For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
CBSE | Class 10 | Exercise 2.4 | Maths | NCERT Exemplar | Polynomials
For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

(i) (–8/3), 4/3

(ii) 21/8, 5/16

(I) Sum of the zeroes = – 8/3

Result of the zeroes = 4/3

P(x) = x2 – (amount of the zeroes) + (result of the zeroes)

Then, at that point,

    \[P\left( x \right)=\text{ }x2\text{ }\text{ }\left( -\text{ }8x \right)/3\text{ }+\text{ }4/3\]

    \[P\left( x \right)=\text{ }3x2\text{ }+\text{ }8x\text{ }+\text{ }4\]

Utilizing parting the center term strategy,

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> 3x2\text{ }+\text{ }8x\text{ }+\text{ }4\text{ }=\text{ }0 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

    \[3x2\text{ }+\text{ }\left( 6x\text{ }+\text{ }2x \right)\text{ }+\text{ }4\text{ }=\text{ }0\]

    \[3x2\text{ }+\text{ }6x\text{ }+\text{ }2x\text{ }+\text{ }4\text{ }=\text{ }0\]

    \[3x\left( x\text{ }+\text{ }2 \right)\text{ }+\text{ }2\left( x\text{ }+\text{ }2 \right)\text{ }=\text{ }0\]

    \[\left( x\text{ }+\text{ }2 \right)\left( 3x\text{ }+\text{ }2 \right)\text{ }=\text{ }0\]

    \[\Rightarrow x\text{ }=\text{ }-\text{ }2,\text{ }-\text{ }2/3\]

(ii) Sum of the zeroes = 21/8

Result of the zeroes = 5/16

P(x) = x2 – (amount of the zeroes) + (result of the zeroes)

Then, at that point,

    \[P\left( x \right)=\text{ }x2\text{ }\text{ }21x/8\text{ }+\text{ }5/16\]

    \[P\left( x \right)=\text{ }16x2\text{ }\text{ }42x\text{ }+\text{ }5\]

Utilizing parting the center term strategy,

    \[16x2\text{ }\text{ }42x\text{ }+\text{ }5\text{ }=\text{ }0\]

    \[16x2\text{ }\text{ }\left( 2x\text{ }+\text{ }40x \right)\text{ }+\text{ }5\text{ }=\text{ }0\]

    \[16x2\text{ }\text{ }2x\text{ }\text{ }40x\text{ }+\text{ }5\text{ }=\text{ }0\]

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> 2x\text{ }\left( 8x\text{ }\text{ }1 \right)\text{ }\text{ }5\left( 8x\text{ }\text{ }1 \right)\text{ }=\text{ }0 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

    \[~\left( 8x\text{ }\text{ }1 \right)\left( 2x\text{ }\text{ }5 \right)\text{ }=\text{ }0\]

    \[\Rightarrow x\text{ }=\text{ }1/8,\text{ }5/2\]

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