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

1.	Find quadratic polynomial whose sum of zeroes are 3/√2,-5√2
Answer» $\bf\huge\blue{\underline{\underline{ Question : }}}$ 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. $\sf\:\implies x^{2} -(\cfrac{3}{\sqrt{2}})x + (-\cfrac{5}{\sqrt{2}})=0$ $\sf\:\implies x^{2} - \cfrac{3x}{\sqrt{2}} - \cfrac{5}{\sqrt{2}}=0$ $\sf\:\implies \cfrac{\sqrt{2}x^{2} - 3x - 5}{2}=0$ $\sf\:\implies \sqrt{2}x^{2} - 3x - 5 = 0 \times 2$ $\sf\:\implies \sqrt{2}x^{2} - 3x - 5 = 0$ $\underline{\boxed{\rm{\purple{\therefore Hence, \:the\:Quadratic\:Polynomial\:is\:\sqrt{2}x^{2} - 3x - 5 = 0.}}}}\:\orange{\bigstar}$

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