Question

if m and n are the zeros of the polynomial p(x)=4x^2+3x+7,find1/m+1/n​

Answer 1

$\textbf{\huge{\underline{Polynomials} : }}$


If m and n are zeros of polynomial then,


$\bold{Sum\:of\:zeros = - \frac{Coefficient\:of\:x}{Coefficient\:of\:x^2}}$


⇒ m + n = - (+ 3)/4

⇒ m + n = - 3/4


$\bold{Product\:of\:zeros = \frac{Constant\:Term}{Coefficient\:of\:x^2}}$


⇒ mn = 7/4


$\textbf{\underline{On solving equations}}$


⇒ 1/m + 1/n = (m + n)/mn

⇒ (- 3/4)/(7/4)

⇒ - 3/4 × 4/7

⇒ - 3/7


$\huge{\boxed{\bold{\underline{Answer} = \frac{-3}{7}}}}$