Question

the roots of quadratic equation 2 X square +2 root 2 X +1=0 are
please answer fast!!!!
​

Answer 1

✪AnSwEr

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

• A polynomial
• 2x²+2√2x+1=0

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

• Factors of the polynomial
• Relationship between cofficient

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

2x²+2√2x+1=0

• we have to spilt the middle term in such a way that the product become 2 and sum become 2√2

2x²+2√2x+1=0

=>2x²+√2x+√2x+1=0

=>√2x(√2x+1)+1(√2x+1)=0

=>(√2x+1) (√2x+1)

=>x=-1/√2 ,-1/√2

Additional Information

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

Then,

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

&

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

Here,

a=2

b=2√2

C=1

☞

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

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

&

$\rightarrow\tt\alpha{\times}\beta{=}\dfrac{1}{2}$

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

Hence,relation verified

Answer 2

Given:

2x²+2√2x+1=0.....(Given Quadratic equation)

To Find:

Roots=?

Solution:

2x²+2√2x+1=0

2x²+√2x+√2x+1=0

√2x(√2x+1) +1(√2x+1) =0

(√2x+1) (√2+1) =0

(√2x+1) =0 OR (√2+1) =0

√2x=-1 or √2 =-1

x= -1/√2 or x = -1/√2