What are the #x#-intercepts of the graph of #y=2x^2+x-10#?

1 Answer
Jim G.
May 3, 2018

#x=-5/2,x=2#

Explanation:

#"to find the intercepts set y = 0"#

#rArr2x^2+x-10=0#

#"using the a-c method to factor the quadratic"#

#"the factors of the product "2xx-10=-20#

#"which sum to + 1 are - 4 and + 5"#

#"split the middle term using these factors"#

#2x^2-4x+5x-10=0larrcolor(blue)"factor by grouping"#

#rArrcolor(red)(2x)(x-2)color(red)(+5)(x-2)=0#

#"take out the "color(blue)"common factor "(x-2)#

#rArr(x-2)(color(red)(2x+5))=0#

#"equate each factor to zero and solve for x"#

#x-2=0rArrx=2#

#2x+5=0rArrx=-5/2#
graph{(y-2x^2-x+10)((x-2)^2+(y-0)^2-0.04)((x+5/2)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}

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