# 4a2 - 11a + 6 = 0 use factoring and the zero-product property to solve the following problem.

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### 1 Answer

The given problem is `4a^2 - 11a + 6 = 0`

In order to factorize first split the coefficient of the middle term -11 as the sum of 2 numbers which give a product of 24. This can be done as -11 = (-8) + (-3).

`4a^2-8a-3a+6=0`

`rArr 4a(a-2)-3(a-2)=0`

`rArr (a-2)(4a-3)=0`

The "Zero Product Property" says that if a*b=0 then a=0 or b=0 (or both a=0 and b=0)

So, for (a-2)=0 we get a=2

and for (4a-3)=0 we get a=3/4

**Therefore, the solutions are a=2, 3/4.**

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