Question

Which of the following tables shows the correct steps to transform x² + 10x + 24 = 0 into the form (x-p)² = q?

[p and q are integers]

Step 1x²+10x+24-1-0-1
Step 2 x²+10x+23 = -1
Step 3 (x+5)=-1

Step 1 x²+10x+24-2=0-2
Step 2 x²+10x+22=-2
Step 3 (x + 5)2 = -2

Step 1 x²+10x+24+2=0+2
Step 2 x²+ 10x+26=2
Step 3 (x+5)=2

Step 1x²10x+24+1=0+1
Step 2 x²+ 10x + 25 = 1
Step 3 (x + 5)2 = 1

Answer 1

option D)

Step 1 : x²+ 10x + 24 + 1 = 0 + 1

Step 2 : x² + 10x + 25 = 1

Step 3 : (x + 5)² = 1

Explanation:

(x-p)² = q

⇒ x² -2(x)(p) + p² = q

⇒ x² -2px + (p² - q) = 0 ---eq(1)

Given:

x² +10x + 24 = 0 ----eq(2)

Comparing eq(1) and eq(2)

-2px = 10x and

p² - q = 24

-2px = 10x

⇒ p =
`(10x)/(-2x)`

⇒ p = -5

p² - q = 24

⇒ (-5)² - q = 24

⇒ 25 - q = 24

⇒ q = 25 - 24

⇒ q = 1

(x-p)² = q :

(x+5)² = 1