Question

Find the roots of the given quadratic equations
1. √2x square -3x -5√2 = 0​

Answer 1

${\huge{\rm{\underline{\underline{Question:–}}}}}$

Q) Find the roots of the given Quadratic Equation

√2x² - 3x - 5√2 = 0

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${\large{\underline{\bf{\star\;Given\;:-}}}}$

• Equation : √2x² - 3x - 5√2 = 0

${\large{\bf{\underline{\star\;To\;Find\;:-}}}}$

• The roots of the Equation .

${\huge{\bf{\underline{\star\;Solution\;:-}}}}$

The standard Quadratic Equation is in the form :

$\boxed{ \sf{a {x}^{2} + bx + c = 0}}$

Compare it with the given Equation ..

$\sf \: a {x}^{2} + bx + c \: \: \rang \lang \: \: \sqrt{2} {x}^{2} - 3x - 5 \sqrt{2}$

Here ,

• a = √2
• b = -3
• c = -5√2

Now ,

Using the Quadratic Formula to find the roots -

$\boxed{ \sf{roots = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} }}$

$\mapsto \rm \: roots = \frac{ - ( - 3) \pm \: \sqrt{ {( - 3)}^{2} - 4( \sqrt{2})( - 5 \sqrt{2} ) } }{2 \times \sqrt{2} }$

$\mapsto \rm \: roots = \frac{3 \pm \: \sqrt{9 + 40} }{2 \sqrt{2} }$

$\mapsto \rm \: roots = \frac{3 \pm \: \sqrt{49} }{2 \sqrt{2} }$

$\mapsto \rm \: roots = \frac{3 \pm 7}{2 \sqrt{2} }$

So ,

First root -

$\rightarrow \rm \: 1st \: root = \frac{3 + 7}{2 \sqrt{2} }$

$\rightarrow \rm \: 1st \: root = \frac{ \cancel{10}}{ \cancel2 \sqrt{2} }$

$\rightarrow \rm \: 1st \: root = \frac{5}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$\longrightarrow \underline{ \boxed{ \frak{ \pink{first \: root = \frac{5 \sqrt{2} }{2}}}}}$

Second root -

$\rightarrow \rm \: 2nd \: root = \frac{3 - 7}{2 \sqrt{2} }$

$\rightarrow \rm \: 2nd \: root = \frac{ - \cancel4}{ \cancel2 \sqrt{2} }$

$\rightarrow \rm \: 2nd \: root = \frac{ - 2}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$\rightarrow \rm \: 2nd \: root = \frac{ - \cancel2 \sqrt{2} }{ \cancel2}$

$\longrightarrow \underline{ \boxed{ \frak{ \pink{second \: root = - \sqrt{2} }}}}$

So ,

The roots of the Equation are $\frak{5√2}{2}$ and -√2 .

_________________________

${\large{\bf{\underline{\star\;Know\;More\;:-}}}}$

• A Quadratic Equation has 2 roots / Zeroes .

• The degree of a Quadratic Polynomial is 2 .

• The roots/Zeroes are those values , which when put in place of the variable , makes the whole Polynomial=0 .

• The roots of a Quadratic Equation can be found using Middle Term Splitting or Quadratic Formula .

Answer 2

Answer:

well you already got the answer