Question

find the roots of quadratic equation√2x²+7x+5√2​

Answer 1

$\small\orange {\sf{Bonjour\ Mate!}}$

☆$\small\green {\sf{Answer }}$☆

√2 x² +7x +5 √2 = 0

⇒ √2 x² + 5x + 2x + 5√2 = 0

⇒ √2x² + 5x + √2*√2*x + 5√2=0

⇒ x(√2x + 5) + √2(√2x + 5) =0

⇒ (x+√2)(√2x+5) = 0

ᴛʜᴀᴛ ɢɪᴠᴇs x= - √2 ᴏʀ x= - 5/√2

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{Find \ the \ roots \ of \ quadratic \. equation}$

$\rm{ \sqrt{2} {x}^{2} + 7x + 5 \sqrt{2} = 0 }$

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$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\rm{\blue{\underline{\red{Roots \ of \ the \ quadratic \ equation \ are:}}}}$

$\rm{\blue{\boxed{\red{ - \frac{5}{ \sqrt{2} } \ and \ - \sqrt{2} }}}}$

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$\sf\large\underline\pink{Given:}$

$\rm{The \ quadratic \ equation \ is}$

$\rm{ \sqrt{2}{x }^{2} + 7x + 5 \sqrt{2} = 0 }$

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$\sf\large\underline\blue{To \ Find}$

$\rm{Roots \ of \ the \ quadratic \ equation}$

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$\green{\underline{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}}$

$\rm{The \ quadratic \ equation \ is}$

$\rm{ \sqrt{2}{x }^{2} + 7x + 5 \sqrt{2} = 0 }$

$\rm{Here ,}$

$\rm{We \ have \ to \ split \ middle \ term \ such }$

$\rm{that }$

$\rm\longrightarrow{Product \ of \ first \ and \ last \ term \ is \ 10}$

$\rm\longrightarrow{Sum \ of \ first \ and \ last \ term \ is \ 7}$

$\rm\implies{ \sqrt{2} {x}^{2} + 2x + 5x + 5 \sqrt{2} = 0}$

$\rm\implies{ \sqrt{2} {x}^{2} + 2x + 5x + 5 \sqrt{2} = 0}$

$\rm\implies{x \sqrt{2}( {x} + \sqrt{2}) + 5(x+ \sqrt{2}) = 0}$

$\rm\implies{ (x \sqrt{2}+5)({x} + \sqrt{2})}$

$\rm\longrightarrow{(x \sqrt{2}+5)=0 \ and \ ({x} + \sqrt{2})=0}$

$\rm\therefore{x \sqrt{2}= -5}$

$\rm\therefore{x \ = \ - \frac{5}{\sqrt{2}}}$

$\rm{And}$

$\rm\therefore{{x} + \sqrt{2}= - \sqrt{2}}$

$\rm{\blue{\underline{\red{Roots \ of \ the \ quadratic \ equation \ are:}}}}$

$\rm{\blue{\boxed{\red{ - \frac{5}{ \sqrt{2} } \ and \ - \sqrt{2} }}}}$

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$\tt\orange{Hope \ it \ Helps \ :))}$