Question

4. Elias was asked to solve a quadratic equation by factoring and his work is shown below. Circle the letter of the step where he has made an error. Then redo the work correctly from that point, using the shaded space. 4 points possible Given x2 – 12x = -20

Аx2 - 12x + 20 = 0
B(x - 4)(x – 5) = 0
С x-4 = 0 OR x-4 = 0
D x = 4 or x = 5 ​

Answer 1

Let's solve

`\\ \sf\longmapsto x^2-12x=-20`

`\\ \sf\longmapsto x^2-12x+20=0`

`\\ \sf\longmapsto x^2-10x-2x+20=0`

`\\ \sf\longmapsto x(x-10)-2(x-20)=0`

`\\ \sf\longmapsto (x-10)(x-2)=0`

`\\ \sf\longmapsto x=10\:or x=2`

Option B

Answer 2

• (B) (x - 4)(x – 5) = 0

Explanation:

He made a mistake at step 2.

• (x - 4)(x - 5) = 0 is incorrect as

it is same as x² - 9x + 20 = 0

It should be:

• (x - 10)(x - 2) = 0 with the end result x = 10 or x = 2