Question

If the Arch is represented by x²/2- x/2-6 = 0 then its zeroes are:
(a)1. - 3
(b)-12
(c)-3,4
(d)3-4​

Answer 1

Answer:

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Step-by-step explanation:

Correct option is

C

3,−2

We find the zeroes by factorizing the equation x

2

−x−6=0 as follows:

x

2

−x−6=0

⇒x

2

−3x+2x−6=0

⇒x(x−3)+2(x−3)=0

⇒(x+2)(x−3)=0

⇒x+2=0,x−3=0

⇒x=−2,x=3.

Hence, the zeroes of the polynomial x

2

−x−6=0 are 3,−2.

Therefore, option C is correct.

Answer 2

Given:

An arc is represented by $\[\frac{{{x^2}}}{2} - \frac{x}{2} - 6 = 0\]$

To find: the zeroes of the given arc.

Solution:

Know that from the question, an arc is represented by $\[\frac{{{x^2}}}{2} - \frac{x}{2} - 6 = 0\]$.

Simplify the given expression.

$\[\frac{{{x^2}}}{2} - \frac{x}{2} - 6 = 0\]$

$\[ \Rightarrow \frac{{{x^2} - x - 12}}{2} = 0\]$

$\[\begin{array}{l} \Rightarrow {x^2} - x - 12 = 0\\ \Rightarrow {x^2} - 4x + 3x - 12 = 0\\ \Rightarrow x\left( {x - 4} \right) + 3\left( {x - 4} \right) = 0\\ \Rightarrow \left( {x + 3} \right)\left( {x - 4} \right) = 0\end{array}\]$

$\[\begin{array}{l} \Rightarrow x + 3 = 0\,or\,x - 4 = 0\\ \Rightarrow x = - 3\,or\,x = 4\end{array}\]$

Therefore, the zeroes of the given arc is $-3,4$.

Hence, the correct answer is option (c). i.e., $-3,4$.