Nikhil expressed the quadratic equation x2+10x+16=0 in the form x2+px+qx+16=0 such that the product of p and q is 16. Choose the correct values of p and q.
p= 2, q= 8
Comparing x2+10x+16=0 to ax2+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
x2+10x+16=0
x2+2x+8x+16=0