Question

9a²-6a+1=0 find the zeros by splitting the middle term
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Answer 1

Answer:

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Step-by-step explanation:

Factoring 9a2-6a+1

The first term is, 9a2 its coefficient is 9 .

The middle term is, -6a its coefficient is -6 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 9 • 1 = 9

Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is -6 .

-9 + -1 = -10

-3 + -3 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -3

9a2 - 3a - 3a - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

3a • (3a-1)

Add up the last 2 terms, pulling out common factors :

1 • (3a-1)

Step-5 : Add up the four terms of step 4 :

(3a-1) • (3a-1)

Which is the desired factorization

therefore a=1/3

Answer 2

Answer:

$9 {a}^{2} - 6a + 1 = 0 \\ \\ = > 9 {a}^{2} - 3a - 3a + 1 \\ \\ = > 3a(3a - 1) - 1(3a - 1) = 0 \\ \\ = > (3a - 1)(3a - 1) = 0 \\ \\ \\ 3a = 1 \\ \\ a = \frac{1 }{3}$

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