Question

If $(mx+7)(5x+n)=p{x}^2+15x+14,\forall xϵR$, then $m+n+p=$

• A. $62$
• B. $-62$
• C. $-58$
• D. $None$

Answer 1

The correct option is C $-58$

Given,

$(mx+7)(5x+n)=p{x}^2+15x+14$

$⟹5m{x}^2+mnx+35x+7n=p{x}^2+15x+14$

On comparing $p=5m,mn+35=15,7n=14$

$⟹n=2$

Also $mn+35=15,m\times 2=-20⟹m=-10$

and $p=5m=5(-10)=-50$

Therefore $m+n+p=2-10-60=-58$