Question

Question 10
Verify whether the following are true or false.
(i) -3 is a zero of x - 3
(ii) $-\frac{1}{3}$ is a zero of 3x + 1
(iii) $-\frac{4}{5}$ is a zero of 4 - 5y
(iv) 0 and 2 are the zeroes of $t^2–t$
(v) -3 is a zero of $y^2+y–6$

Answer 1

(i) False. Zero of x – 3 is 3.
$[\because x-3=0\Rightarrow x=3]$

(ii) True. Zero of 3x+1 is$-\frac{1}{3}$.
$[\because 3x+1=0\Rightarrow x=\frac{-1}{3}]$

(iii) False. Zero of 4 - 5y is$\frac{4}{5}$.
$[\because 4-5y=0\Rightarrow y=\frac{4}{5}]$

(iv)True.
$t^2–2t=t(t–2)$
Hence, zeroes of $t^2–2t$ are 0 and 2.

(v) True.
$y^2+y–6=y^2+3y–2y–6$ [ by splitting middle term]
$=y(y+3)–2(y+3)$
$=(y-2)(y+3)$ ...(i) [equating equation(i) equal to zero]
Hence, the zeroes of $y^2+y–6$ are 2 and -3.