Verify whether the following are true or false:(i) –3 is a zero of x

1.	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
Answer» (i) –3 is a zero of x – 3 False Zero of x – 3 is given by, x – 3 = 0 ⇒ x=3 (ii) – 1/3 is a zero of 3x + 1 True Zero of 3x + 1 is given by, 3x + 1 = 0 ⇒ 3x = – 1 ⇒ x = – 1/3 (iii) – 4/5 is a zero of 4 –5y False Zero of 4 – 5y is given by, 4 – 5y =0 ⇒ – 5y = – 4 ⇒ y = 4/5 (iv) 0 and 2 are the zeroes of t² – 2t True Zeros of t² – 2t is given by, t² – 2t = t(t – 2) = 0 ⇒ t = 0 or 2 (v) –3 is a zero of y² + y – 6 True Zero of y² + y – 6 is given by, 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

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

Answer»

(i) –3 is a zero of x – 3

False

Zero of x – 3 is given by,

x – 3 = 0

⇒ x=3

(ii) – 1/3 is a zero of 3x + 1

True

Zero of 3x + 1 is given by,

3x + 1 = 0

⇒ 3x = – 1

⇒ x = – 1/3

(iii) – 4/5 is a zero of 4 –5y

False

Zero of 4 – 5y is given by,

4 – 5y =0

⇒ – 5y = – 4

⇒ y = 4/5

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

True

Zeros of t² – 2t is given by,

t² – 2t = t(t – 2) = 0

⇒ t = 0 or 2

(v) –3 is a zero of y² + y – 6

True

Zero of y² + y – 6 is given by,

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