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Question

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.


A

p = 1, q = 16

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B

p = -2, q= -8

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C

p= 2, q= 8

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D

p= 2, q= 5

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Solution

The correct option is C

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


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