Verify whether the following are true or false: (i) -3 is a zero of x - 3 (ii) - 1/3 is a zero of 3x + 1 (iii) - 4/5 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

Solution

(i) –3 is a zero of x – 3

The given statement is False

Zero of x – 3 can be determined as

x – 3 = 0

⇒ x=3

(ii) – 1/3 is a zero of 3x + 1

The given statement is True

Zero of 3x + 1 can be determined as

3x + 1 = 0

⇒ 3x = – 1

⇒ x = – 1/3

(iii) – 4/5 is a zero of 4 –5y

The given statement is False

Zero of 4 – 5y can be determined as

4 – 5y =0

⇒ – 5y = – 4

⇒ y = 4/5

(iv) 0 and 2 are the zeroes of t2 – 2t

The given statement is True

Zeros of t2 – 2t can be determined as

t2 – 2t = t(t – 2) = 0

⇒ t = 0 or 2

(v) –3 is a zero of y2 + y – 6

The given statement is True

Zero of y2 + y – 6 can be determined as

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

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