Q. 34.0( 277 Votes )

Verify whether th

Answer :

For any value of x, say a, to be a zero of polynomial p(a) = 0


Keeping that in mind,

(i) Here p(x)= 3x + 1 ,  for x = -1/3


Therefore, x = –1/3 is a zero of polynomial p(x) = 3x + 1


(ii) here p(x) = 5x - π, for x = 4/5,


Since,  

Therefore, x = 4/5  is not a zero of polynomial p(x) = 5x - π


(iii) If x = 1 and x = -1 are zeros of polynomial p(x) = x2 - 1 then p (1) and p (-1) should be 0


At, p (1) = (1)2 – 1 = 0 and,


At, p (-1) = (-1)2 – 1 = 0


Hence, x = 1 and -1 are zeros of polynomial p (x) = x2 - 1


(iv) If x = -1 and x = 2 are zeros of polynomial p(x) = (x + 1) (x – 2) then p (-1) and p (2) should be 0


At, p (-1) = (-1 + 1) (- 1 – 2) = 0 (-3) = 0 and,


At, p (2) = (2 + 1) (2 – 2) = 3 (0) = 0


Hence, x = -1 and x = 2 are zeros of polynomial p (x) = (x + 1) (x – 2)


(v) If x = 0 is a zero of polynomial p (x) = x2


Then, p (0) should be zero


Here, p (0) = (0)2 = 0


Hence, x = 0 is the zero of the polynomial p (x) = x2


(vi) If x = is a zero of the polynomial p(x) = lx + m then p () should be 0


 


Therefore, x = is the zero of the polynomial p(x) = l x + m


(vii) If x = and x = are zeros of the polynomial p(x) = 3 x2 – 1, then


p() and p() should be 0


At, p () = 3 ()2 – 1


= 3 () – 1


= 1 – 1 = 0 and,


At, p () = 3 ()2 – 1


= 3 () – 1


= 4 – 1 = 3


Therefore, x = is a zero of the polynomial p(x) = 3x2 + 1


But, x = is not a zero of the polynomial


(viii) If x = is a zero of polynomial p (x) = 2x + 1 then p(1/2) should be zero


At, p () = 2 () + 1


= 1 + 1 = 2


Therefore, x = is not a zero of given polynomial p(x) = 2x + 1

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