Question

find quadratic polynomial whose sum of zeroes are 3/√2,-5√2​

Answer 1

$\bf\huge\blue{\underline{\underline{ Question : }}}$

Find quadratic polynomial whose sum of zeroes are 3/√2 and product of the zeroes are -5√2.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

$\tt\:\rightarrow Sum\:of\:the\:zeroes : \alpha + \beta = \cfrac{3}{\sqrt{2}}$

$\tt\:\rightarrow Product\:of\:the\:zeroes : \alpha \beta =- \cfrac{5}{\sqrt{2}}$

★ To find,

• The Quadratic Polynomial.

★ Let,

The form of Quadratic Polynomial is :

$\boxed{\rm{\red{ x^{2} -(\alpha+\beta)x + \alpha\beta = 0}}}$

• Substitute the zeroes.

$\sf\:\implies x^{2} -(\cfrac{3}{\sqrt{2}})x + (-\cfrac{5}{\sqrt{2}})=0$

$\sf\:\implies x^{2} - \cfrac{3x}{\sqrt{2}} - \cfrac{5}{\sqrt{2}}=0$

$\sf\:\implies \cfrac{\sqrt{2}x^{2} - 3x - 5}{2}=0$

$\sf\:\implies \sqrt{2}x^{2} - 3x - 5 = 0 \times 2$

$\sf\:\implies \sqrt{2}x^{2} - 3x - 5 = 0$

$\underline{\boxed{\rm{\purple{\therefore Hence, \:the\:Quadratic\:Polynomial\:is\:\sqrt{2}x^{2} - 3x - 5 = 0.}}}}\:\orange{\bigstar}$