Math, asked by mayanksharma401, 8 months ago

Find the difference of the roots of the quadratic equation 25x2 - 10x + 1 = 0​

Answers

Answered by Abhishek474241
5

AnSwEr

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

  • A polynomial
  • 25X²-10x+1=0

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

  • Factors of the polynomial
  • Relationship between cofficient

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

25x2 - 10x + 1 = 0

  • we have to spilt the middle term in such a way that the product become 25 and sum become -10

25x2 - 10x + 1 = 0

=>25x²-5x-5x+1=0

=>5x(5x-1)-1(5x-1)=0

=>(5x-1) (5x-1)

=>x=1/5,1/5

Their differences is 0

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=1

b=-10

C=1

\rightarrow\tt\alpha{+}\beta{=}\dfrac{-10}{1}

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

&

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

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

Hence,relation verified

Answered by Anonymous
5

Step-by-step explanation:

Given :-

  • Quadratic equation 25x2 - 10x + 1 = 0

To Find :-

  • Find the difference of the roots

According to the quadratic formula

  • The quadratic formula is simply just ax^2+bx+c = 0 in terms of x. So the roots of ax^2+bx+c = 0 would just be the quadratic equation, which is: (-b+-√b^2-4ac) / 2a.

Solution:-

==> 25x^2 - 10x + 1 = 0

==> 25x^2 -5x -5x + 1 =0

==> 5x (5x-1) - 1(5x -1) =0

==> (5x - 1) (5x - 1) =0

x = 1/5 ,1/5

That's proved They have no difference.

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