Question

Nikhil expressed the quadratic equation $x^2+10x+16=0$ in the form $x^2+px+qx+16=0$ such that the product of p and q is 16. Choose the correct values of p and q.

• A. p = 1, q = 16
• B. p = -2, q= -8
• C. p= 2, q= 8
• D. p= 2, q= 5

Answer 1

The correct option is C

p= 2, q= 8

Comparing $x^2+10x+16=0$ to $a{x}^2+bx+c=0$, we have a=1 , b=10 and c=16
Now, we need to find two numbers whose product is 16 and whose sum is 10 as p + q = 10
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 10 is the third pair.
Hence, p and q can take the values of either 2 or 8. As per the given options, p = 2 and q = 8 is correct.
Identifying the pair, we rewrite the given quadratic equation as
$x^2+10x+16=0$
$x^2+2x+8x+16=0$