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 are:

$(1,16),(-1,-16),(2,8),(-2,-8),(4,4),(-4,-4)$
Of these pairs, the pair that gives the sum $10$ is the pair, $(2,8)$
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
$x^2+10x+16=0$
$\Rightarrow x^2+2x+8x+16=0$