Find the zeros of the function algebraically. f(x)=2x2−3x−54

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rodclassique4r · Accepted Answer

Step 1  Given function is f(x)=2x2−3x−54  To find the zeroes of the function.  Solution:  Finding zeroes of the given function.  2x2−3x−54=0  2x2−12x+9x−54=0  2x(x−6)+9(x−6)=0  (x−6)(2x+9)=0  (x−6)=0 or (2x+9)=0  x=6 or x=−92  Step 2  Hence, zeroes of the given function are x={−92,6}

Fasaniu · Accepted Answer

Simplifying   2x2±3x±54=0  Reorder the terms:  −54±3x+2x2=0  Solving  −54±3x+2x2=0  Solving for variable &quot;x&quot;.  Factor a trinomial.  (−9±2x)(6±1x)=0

karton · Accepted Answer

Factor the expression by grouping. First, the expression needs to be rewritten as $2 x^{2} + a x + b x - 54$ . To find a and b, set up a system to be solved.
a+b=-3
ab=2(-54)=-108
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -108.
The solution is the pair that gives sum -3.
a=-12
b=9
Rewrite $2 x^{2} - 3 x - 54$ as $(2 x^{2} - 12 x) + (9 x - 54)$
Factor out 2x in the first and 9 in the second group.
2x(x-6)+9(x-6)
Factor out common term x-6 by using distributive property.
(x-6)(2x+9)

Find the zeros of the function algebraically. f(x)=2x^{2}-3x-54

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