How do you factor the trinomial #4x^2 - 21x + 5 = 0#?
1 Answer
Mar 10, 2018
Explanation:
#"using the a-c method of factorising a quadratic"#
#"consider the factors of "(4xx5)" which sum to - 21"#
#"the factors of + 20 which sum to - 21 are - 20 and - 1"#
#"splitting the middle term gives"#
#4x^2-20x-x+5larrcolor(blue)"factor by grouping"#
#=color(red)(4x)(x-5)color(red)(-1)(x-5)#
#"take out common factor "(x-5)#
#(x-5)(color(red)(4x-1))#
#rArr4x^2-21x+5=(x-5)(4x-1)#
#"to solve the equation"#
#(x-5)(4x-1)=0#
#"equate each of the factors to zero and solve for x"#
#x-5=0rArrx=5#
#4x-1=0rArrx=1/4#
