Question

Find the quadratic whose sum is (-20) and product of zeroes is 190?

Answer 1

$\\\begin{gathered}\mathfrak{Given}\begin{cases} {\sf{Sum \: of \: Zeros=(-20)}} \\ \sf {Product \: of \: zeros=190}\end{cases}\end{gathered}$

$\\\sf{Let \: the \: two \: zeros \: of \: Quadratic \: polynomial \: be \: \: \alpha \: and \: \beta }$

• $\\\sf Sum~ of ~Zeros(\alpha+\beta)=(-20)$
• $\\\sf Product ~of ~zeros(\alpha\beta)=190$

$\\ \sf{If \: a \: a nd \: b \: a re \: the \: zeros \: of \: Quadratic \: polynomial \: f(x) \: then}$

${→ f(x)= x²-(Sum \: of \: zeros)x+(Product \: of \: zeros)}$

$→f(x) = {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta )$

$→f(x) = {x}^{2} - ( - 20 )x + 190$

$→f(x) = {x}^{2} + 20 x + 190$

${\therefore \text{ the Required Quadratic polynomial}} \\ \bf \: f(x) = {x}^{2} + 20x + 190$