Question

Find the quadratic polynomial whose sum and product of the zeros are minus 1 by 4 and 1 by 3

Answer 1

$\tt{\underline{\color{teal}{Given}}}{\bigstar}$

• $\tt{Sum \: of \: the \: zeros \: = \frac{1}{4} }$
• $\tt{Product \: of \: the \: zeros \: = \frac{1}{3} }$

$\tt{\underline{\color{teal}{To \: Find}}}{\bigstar}$

• $\tt{The \: quadratic \: polynomial}$

$\tt{\underline{\color{teal}{Solution}}}{\bigstar}$

We know that

Formula for Quadratic Polynomial

$\tt{ {x}^{2} + (sum \: of \: the \: zeros )x + product \: of \: the \: zeros}$

$\tt{\implies {x}^{2} + \frac{1}{4}x + \frac{1}{3} }$

Hence the required polynomial is$\tt{ {x}^{2} + \frac{1}{4}x + \frac{1}{3} }$

$\tt{\underline{\color{teal}{ThankYou}}}{\bigstar}$

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• sum of zeros = $\sf\dfrac{1}{4}$
• product of zeros = $\sf\dfrac{1}{3}$

$\sf{\bold{\green{\underline{\underline{To\: Find}}}}}$

• The quadratic polynomial

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\bold{\red{\boxed{Quadratic\:polynomial }}}}$

$\sf{\bold{\red{\boxed{ \: = \:x^2 \: +\: sum \: of \: zeros \: x + product\: of \: zeros }}}}$

$\sf\implies Quadratic \: polynomial = x^2 + \dfrac{1}{3}x + \dfrac{1}{4}$