Question

The quadratic polynomial whose sum of zeroes -3 and product of zeroes 2 is:

Answer 1

Given:-

• sum of zeroes = -3

• product of zeroes = 2

To find:-

• The quadratic polynomial

Solution:-

• $\sf{ \alpha + \beta = -3}$

• $\sf{ \alpha \beta = 2}$

The required polynomial:-

★ General Equation:-

$\bold{\underline{\underline{\boxed{\sf{\red{\dag \; x^2 - (sum \; of \; zeroes)x + (product of zeroes) = 0}}}}}}$

$\implies \sf{x^2 - (-3)x + (2) = 0}$

$\implies \sf{x^2 +3x + 2 = 0}$

$\rule{200}{2}$

Answer 2

Given ,

Sum of roots (α + β) = -3

Product of roots ( α × β) = 2

We know that ,

$\large \sf \fbox{ {(x)}^{2} - ( \alpha + \beta )x + ( \alpha × \beta )}$

Thus ,

$\Rightarrow \sf {(x)}^{2} - ( - 3)x + 2 \\ \\ \Rightarrow \sf {(x)}^{2} + 3x + 2 = 0$

$\therefore \sf \bold{ \underline{The \: polynomial \: is \: {(x)}^{2} + 3x + 2}}$