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

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
$(1,16),(-1,-16),(2,8),(-2,-8),(4,4)\text{and}(-4,-4)$

Of these pairs , the pair that gives the sum 10 is $(2,8)$.

Hence, p and q can take the values of either 2 or 8.

We can rewrite the given quadratic equation as
$x^2+10x+16=0$ as $x^2+2x+8x+16=0$.