Question

Write $x^2$ +8x+16 =0 in the form $x^2$ +px+qx+16 =0 such that p x q = 16

• A. p = 8, q = 2
• B. p = -8, q = -2
• C. p = 2, q = 6
• D. p = -2, q = -8

Answer 1

The correct option is C

p = 2, q = 6

Comparing $x^2$ +8x+16 =0 to a$x^2$ + bx+ c = 0, we have a=1 , b=8 and c=16

Now, we need to find two numbers whose product is 16 and whose sum is 8

Pairs of numbers whose product is 16

1,16

-1,-16

2,8

-2,-8

4,4

-4,-4

Of these pairs , the pair that gives the sum 8 is the fifth pair

Identifying the pair, we rewrite the given quadratic equation as

$x^2$ +8x+16= $x^2$ +4x+4x+16

$x^2$ +4x+4x+16=0