Verify whether the following are true or false:
(i) –3 is a zero of x – 3
(ii) is a zero of 3x + 1
(iii) is a zero of 4 –5y
(iv) 0 and 2 are the zeroes of t2 – 2t
(v) –3 is a zero of y2 + y – 6
(i) –3 is a zero of x – 3
False because zero of x – 3 = 3 ∵ x – 3 = 0 ⇒ x=3
(ii) is a zero of 3x + 1
True because zero of 3x + 1 = – 1/3 ∵ 3x + 1 = 0 ⇒ x = – 1/3
(iii) is a zero of 4 –5y
False because zero of 4 – 5y is 4/5 ∵ 4 – 5y =0 ⇒ – 5y = – 4 ⇒ y = 4/5
(iv) 0 and 2 are the zeroes of t2 – 2t
T2 – 2t = t(t – 2) = 0 ⇒ t = 0 or 2
Hence the zero of the polynomial are 0 and 2 . the given statement is true.
(v) –3 is a zero of y2 + y – 6
y2 + y – 6 = 0
⇒ y2 + 3x – 2x – 6 = 0
⇒ y (y + 3) – 2(x + 3) = 0
⇒ (y – 2) (y + 3) =0
⇒ y = 2 or – 3
Hence – 3 is one of the zero of the polynomial. The given statement is true.