Question

Please help me with this quadratic equation question! I always give out 5 stars, thanks and brainliest to people that help me with a good explanation.
Find the values of p and q given that 12x² - 13x - 7175 = (x-p) (qx + 287)

Answer 1

Answer:

$p=25,\\q=12$

Step-by-step explanation:

In $(ax+b)(cx+d)=acx^2+bcx+dax+bd$, notice the third term of the quadratic in standard form is formed entirely by $b\cdot d$.

Therefore, in $12x^2 - 13x - 7175 = (x-p) (qx + 287)$:

$-p\cdot287=-7175,\\-p=\frac{-7175}{287},\\p=\fbox{ 25 }$.

Now that we found $p$, we must find $q$. The first term of the quadratic in standard form is formed entirely by $ax\cdot cx$. Therefore:

$1\cdot q=12, \\q=\fbox{ 12 }$.