Question

Jack rewrites the quadratic 9x^2 - 30x - 42 in the form of (ax + b)^2 + c, where a, b, and c are all integers. What is ab?

Answer 1

Answer:

- 15

Step-by-step explanation:

Let 9x^2 - 30x - 42 = D

= > 9x^2 - 30x = D + 42

Completing square on LHS:

= > 9x^2 - 30x = D + 42

Adding 25 to both sides:

= > 9x^2 - 30x + 25 = D + 42 + 25

= > ( 3x )^2 - 2( 5*3x ) + 5^2 = D + 67

= > ( 3x - 5 )^2 = D + 67

= > ( 3x - 5 )^2 - 67 = D

Comparing the result and given statements :

a = 3 ; b = - 5 ; c = - 67

Hence, ab = - 5 * 3 = - 15