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Verify whether the follo wing are zeroes of the polyrwmial. indicated against them. . l (i) p(x) = 3x + l, x = - 3 (lli) p(x) = z2 - 1, x = 1, - 1 (v) p(x) • %', x = 0 (ii} p(x) = 6x - n, x = - 5 (iv) p(x) = (x + l)(x - 2), % = - 1, 2 (vi) p(x) •.lz + m. i=- 7 P OLYNOMIALS 29 (vu) p(%) = 3,_2 - 1, z = - J3 , J3 (viii) p(z) = 2z + l, z = . 2

Verify whether the follo wing are zeroes of the polyrwmial. indicated against them.

. l
(i) p(x) = 3x + l, x = - 3
(lli) p(x) = z2 - 1, x = 1, - 1

(v) p(x) • %', x = 0

(ii} p(x) = 6x - n, x = -
5
(iv) p(x) = (x + l)(x - 2),
% = - 1, 2
(vi) p(x) •.lz + m. i=- 7





P OLYNOMIALS 29

(vu) p(%) = 3,_2 - 1, z = - J3 , J3

(viii) p(z) = 2z + l, z = .
2

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
8 months ago
(i) p(-i) = 3 )( (-i) + 1 .. - 1 + 1= 0 Hence, % = - iis a zero of the polynomial p(z). (ii) p (-) = 5 )( :- 1t = 4 - 1t 0 Hence, z = iis not a zero of the polynomial p(%), (iii) p(l) = 1- 1c 0 and p(- 1) = 1- 1= 0 Hence, z = 1 and % = - 1 are zeroes of the polynomial p(%). (iv) p(- 1) = (-1 + lX- 1- 2) = o and p(2) = (2 + 1) (2 - 2) = 0 Hence, z = - 1 and z = 2 are zeroes of the polynomial p(%). (v) p(O) = 0. Hence, z = 0 is a zero of the polynomial /h). (vi) p (- 7) ;a l •(- 7) + m = - m + m = 0 Hence, % = - 7 is a zero of the polynomial p(%). (ui.i) p (- }a) = 3 )( i- 1c: 1- 1 = 0 and p (rs) = 3 x :- 1 • 4 - 1= 3 O 30 Hence, x = - .J3 is a zero and z • .J3 of the polynomial p(.%). (uiii) p (i) = 2 >< + 1 = l + 1 = 2 0 is not a zero Hence, z = iis not a zero of the polynomial p(x).

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