Question

Verify that 3,-1 and -1/3 are the zeroes of the cubic polynomial p (x)= 3xcube-5xsquare-11x-3, and then verify the relationship between the zeroes and the coefficient.

Class 10th

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Answer 1

Hey!!!

As promised I am here to help you

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Refer to the attachment

There are 3 pages

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Method Source : NCERT

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Answer 2

Heya mate,
here is your answer,
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$p(x) = {3x}^{3 } - {5x}^{2} - 11x - 3$
● Verifying zeroes :-
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=> At x = 3 ,
$p(3) = 3 ({3})^{3} - 5( {3})^{2} - 11(3) - 3 \\ = 81 - 45 - 33 - 3 \\ = 0$
Since p (3) = 0
Hence , 3 is zero of p (x)

••••••••••••••••••••••

=> At x = -1
$p( - 1) = 3 {( - 1)}^{3} - 5 {( - 1)}^{2} - 11( - 1) - 3 \\ = - 3 - 5 + 1 - 3 \\ 0$
Since p (-1) = 0
Hence , -1 is zero of p (x)

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=> At x = -1/3

$p( \frac{ - 1}{3} ) = 3 {( \frac{ - 1}{3} )}^{3} - 5 {( \frac{ - 1}{3}) }^{2} - 11( \frac{ - 1}{3} ) - 3 \\ = \frac{ - 1}{9} - \frac{5}{9} + \frac{11}{3} - 3 \\ = \frac{ - 1 - 5 + 33 - 27}{9} \\ = \frac{ - 33 + 33}{ 9} \\ = 0$
Since p (-1/3) = 0
Hence, -1/3 is zero of p (x)

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● Verifying relationship between zeroes and coefficients
( Refer pic for it )

thanks !!!!

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