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Factor the quadratic equation:

{7x}^(2) - 9x + 2


User Kurt UXD
by
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2 Answers

0 votes

Answer:

7x²-9x+2 = 7(x-2/7)(x-1)

explanation

7x²-9x+2=0

b²-4ac = (-9)²-4(7*2)= 81-56=25

Δ=25

Δ is strictly positive, the equation 7x²−9x+2=0

admits two solutions.

(-b-√Δ)/2a =(9-5)/14 = 4/14 =2/7

(-b+√Δ)/2a =(9+5)/14=14/14=1

solution: x1=2/7; x2=1

factorization:7(x-2/7)(x-1)

User John Faulkner
by
7.6k points
4 votes

Answer:


(7x-2)(x-1)

Explanation:

To factor a quadratic expression in the form ax² + bx + c, we can start by finding two numbers that multiply to 'ac' (the product of 'a' and 'c') and sum to 'b.'

In the case of 7x² - 9x + 2, the values of 'a', 'b' and 'c' are:

  • a = 7
  • b = -9
  • c = 2

The product of 'a' and 'c' is 14, so we need to find two numbers that multiply to 14 and add up to -9.

The factor pairs of 14 are 1 & 14, and 2 & 7. Therefore, the two numbers are -2 and -7 as:


  • (-2)* (-7)=14

  • (-2)+(-7)=-9

Rewrite 'b' as the sum of these two numbers:


7x^2-7x-2x+2

Next, factor the first two terms and the last two terms separately:


7x(x-1)-2(x-1)

Factor out the common term (x - 1):


(7x-2)(x-1)

Therefore, the factored form of the given quadratic expression is:


\Large\boxed{\boxed{(7x-2)(x-1)}}

User TechnicalViking
by
8.1k points

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