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
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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
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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.
Given:
An arc is represented by [tex]\[\frac{{{x^2}}}{2} - \frac{x}{2} - 6 = 0\][/tex]
To find: the zeroes of the given arc.
Solution:
Know that from the question, an arc is represented by [tex]\[\frac{{{x^2}}}{2} - \frac{x}{2} - 6 = 0\][/tex].
Simplify the given expression.
[tex]\[\frac{{{x^2}}}{2} - \frac{x}{2} - 6 = 0\][/tex]
[tex]\[ \Rightarrow \frac{{{x^2} - x - 12}}{2} = 0\][/tex]
[tex]\[\begin{array}{l} \Rightarrow {x^2} - x - 12 = 0\\ \Rightarrow {x^2} - 4x + 3x - 12 = 0\\ \Rightarrow x\left( {x - 4} \right) + 3\left( {x - 4} \right) = 0\\ \Rightarrow \left( {x + 3} \right)\left( {x - 4} \right) = 0\end{array}\][/tex]
[tex]\[\begin{array}{l} \Rightarrow x + 3 = 0\,or\,x - 4 = 0\\ \Rightarrow x = - 3\,or\,x = 4\end{array}\][/tex]
Therefore, the zeroes of the given arc is [tex]-3,4[/tex].
Hence, the correct answer is option (c). i.e., [tex]-3,4[/tex].