Question

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✴ Find the Quadratic equations , if given here two roots are 1/3 and 1/5...?​

Answer 1

$\large{\underline{\underline{\mathfrak{\sf{\green{Answer-}}}}}}$

$\sf{\color{blue}{x^2-\dfrac{8}{15}x+\dfrac{1}{15}}}$

$\large{\underline{\underline{\mathfrak{\sf{\green{Explanation-}}}}}}$

$\begin{lgathered}\bold{Given\:roots} \begin{cases}\sf{\dfrac{1}{3}} \\ \\ \sf{\dfrac{1}{5}}\end{cases}\end{lgathered}$

$\orange{\boxed{\boxed{\pink{\underline{\red{\mathfrak{To\:find-}}}}}}}$

• Quadratic equation or polynomial.

$\orange{\boxed{\boxed{\pink{\underline{\red{\mathfrak{Formula\:used-}}}}}}}$

• $\purple{\sf{x^2-Sx+P}}$

$\orange{\boxed{\boxed{\pink{\underline{\red{\mathfrak{Solution-}}}}}}}$

★ Sum of zeroes ( roots ) :

$\implies$ $\sf{\dfrac{1}{3}+\dfrac{1}{5}}$

By taking LCM,

$\implies$ $\sf{\dfrac{5+3}{15}}$

$\implies$ $\sf{\dfrac{8}{15}}$

★ Product of zeroes ( roots ) :

$\implies$ $\sf{(\dfrac{1}{3})(\dfrac{1}{5})}$

$\implies$ $\sf{\dfrac{1}{15}}$

$\rule{200}2$

Now, put the values of sum of roots and product of roots in the formula :

$\purple{\sf{x^2-Sx+P}}$

$\begin{lgathered}\bold{Here} \begin{cases}\sf{\red{S}\:refers\:to\:sum\:of\:roots} \\ \sf{\red{P}\:refers\:to\:product\:of\:roots}\end{cases}\end{lgathered}$

$\large{\color{blue}{⟹}}$ $\large{\sf{\boxed{\color{blue}{x^2-\dfrac{8}{15}x+\dfrac{1}{15}}}}}$

$\rule{200}2$

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#BAL

Answer 2

Step-by-step explanation:

sum of zeroes = 8/15

product of zeroes=1/15

x^2+ sx-p

x^2 +8/15x-1/15