Respuesta :
Answer:
the zeros as x = 5 or x = -6 . SO the correct option is Option B.
Step-by-step explanation:
i) the zeros of any expression of f(x) is found by equating f(x) to zero and then solving for x.
ii) therefore to find the zeros ( or roots) of the given expression we can write f(x) = [tex]x^{2} + x - 30 = 0[/tex]
iii) therefore [tex]x^{2} + x - 30 = 0[/tex] ⇒ [tex]x^{2} + 6x - 5x - 30 = 0[/tex] .... from visual observation
therefore we can write [tex]x( x + 6) -5(x + 6) = 0[/tex] ⇒ [tex](x - 5)(x + 6) = 0[/tex]
therefore either x - 5 = 0, or, x + 6 = 0 if the above equation is to be true.
iv) therefore solving for x we get the zeros as x = 5 or x = -6. So the correct option is Option B.
Answer:
Therefore the zeros of
[tex]f(x)=x^{2}+x-30[/tex]
are
[tex]x=-6\ and\ x= 5[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=x^{2}+x-30[/tex]
To Find:
Zeros of the function.
Solution:
Zeros of Polynomial or function:
Zeros of the polynomial means while substituting the value of X in the polynomial you will get the value of the polynomial or function equals to Zero.
Hence to find a value of zeros , the value of function should be zero.
Therefore,
f(x) =0
[tex]x^{2}+x-30=0[/tex]
To find the value of 'x' we need to factorize the above quadratic equation.
First is to remove the factor of -30 such that when you add the factors you should get one.
-30 = 6 × -5
6 - 5 = 1
Hence by splitting the middle term we get
[tex]x^{2}+6x-5x-30=0\\x(x+6)-5(x+6)=0\\(x+6)(x-5)=0\\x+6=0\ or\ x-5=0\\x=-6\ or\ x=5[/tex]
Therefore the zeros of
[tex]f(x)=x^{2}+x-30[/tex]
are
[tex]x=-6\ and\ x= 5[/tex]
