Question

X-4√2x+6=0 find the roots of the equation​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A polynomial
• X²-4√2x+6

${\sf{\green{\underline{\large{To\:Verify}}}}}$

• Relationship between cofficient
• Roots Or zeroes

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Roots

• Spilt the middle term in such a way that the
• product become 6 and sum become 4√2

X²-4√2x+6

=>X²-3√2x-√2x+6

=>x(x-3√2)-√2(x-3√2)

=>(x-3√2) (x-√2)

=>x=3√2,√2

Additional Information

Let the zeroes of the polynomial be$\tt\alpha{and}\beta$

Then,

$\tt\alpha{+}\beta{=}\frac{-b}{a}$

&

$\tt\alpha{\times}\beta{=}\frac{c}{a}$

Here,

a=1

b=-4√2

C=6

☞

$\tt\alpha{+}\beta{=}\dfrac{4\sqrt{2}}{1}$

$\tt\alpha{+}\beta{=}\dfrac{Cofficient\:of\:X}{Cofficient\:of\:x^2}=$

&

$\tt\alpha{\times}\beta{=}\dfrac{6}{1}$

$\tt{\large\alpha{\times}\beta{=}\dfrac{Constant\:term}{Cofficient\:of\:x^2}}$

Hence,relation verified

Answer 2

Given ,

The polynomial is x² - 4√2x + 6

By middle term splitting method ,

$\Rightarrow \sf {(x)}^{2} - 3 \sqrt{2} x - \sqrt{2} x+ 6 = 0 \\ \\ \Rightarrow \sf x(x - 3 \sqrt{2} )- \sqrt{2} (x - 3 \sqrt{2} ) = 0 \\ \\ \Rightarrow \sf x - \sqrt{2} = 0 \: \: or \: \: x - 3 \sqrt{2} = 0 \\ \\ \Rightarrow \sf x = \sqrt{2} \: \: or \: \: x = 3 \sqrt{2}$

$\therefore \sf \bold{ \underline{The \: roots \: are \: \sqrt{2} \: and \: 3 \sqrt{2} }}$