Factor the quadratic equation: {7x}^(2) - 9x + 2 ​

Question

Factor the quadratic equation:

`{7x}^(2) - 9x + 2`
​

Answer 1

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)

Answer 2

`(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)}}`