Question

Find the quadratic polynomial whose sum of the zeros is -5 and product of the zeros is 4

Answer 1

Answer:

Step-by-step explanation:

Answer 2

AnswEr :

$\bf{\Large{\underline{\underline{\tt{Given\::}}}}}}$

Sum of the zeroes is -5 and Product of the zeroes is 4.

$\bf{\Large{\underline{\underline{\tt{To\:find\::}}}}}}$

The quadratic polynomial.

$\bf{\Large{\underline{\underline{\rm{\red{Explanation\::}}}}}}}$

$\bf{\large{\underline{\tt{\green{\blacksquare{Sum\:of\:the\:zeroes\::}}}}}}$

$\longrightarrow\tt{\alpha +\beta \:=\:\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2} } }\\\\\\\\\longrightarrow\tt{\green{\alpha +\beta \:=\:-5}}$

$\bf{\large{\underline{\tt{\green{\blacksquare{Product\:of\:the\:zeroes\::}}}}}}$

$\longrightarrow\tt{\alpha \times \beta \:=\:\dfrac{Constant\:term}{Coefficient\:of\:x^{2} } }\\\\\\\\\longrightarrow\tt{\green{\alpha \times \beta \:=\:4}}$

$\bf{\large{\underline{\underline{\rm{The\:quadratic\:polynomial\:rquired\:are\::}}}}}$

$\leadsto\sf{\green{x^{2} -(sum\:of\:the\:zeroes)x+(product\:of\:zeroes)=0}}\\\\\\\leadsto\sf{x^{2} -(-5)x+4=0}\\\\\\\leadsto\sf{\red{x^{2} +5x+4=0}}$