Question

8x2-√2x7=0 find the roots its very urgent

Answer 1

Answer:

Step-by-step explanation:

Method to find solution of a quadratic equation by factorisation:

To find the solution of a quadratic equation by factorization method we use following  steps:

Write the given quadratic equation in standard form ax² + bx + c =0, and find the values of a, b and c.

Multiply a and c and split ac into prime factors. Then find two numbers p and q such that p-q = b  (if Sign of c is negative -ve).

Write the constant b of ax² + bx + c =0, as (p-q) and then factorise it.

Equate each factor to zero  and find the values of x.

SOLUTION:

a)Given quadratic equation is 8x² - 22x - 21= 0.

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 8 , b= -22 , c= -21

Now,ac= 8 × -21= -168

Here, c have negative sign so we have to find the factors of  168 whose difference is - 22. Such factors 28 and 6

8x² - 22x - 21= 0

8x² - 28x +6x  -21=0

4x (2x - 7) + 3(2x -7)= 0

(4x+3) ( 2x-7) = 0

(4x+3) = 0   or  ( 2x-7) = 0

4x = 0-3   or 2x= 0+7

x = -¾,    x = 7/2

Hence, roots of equation 8x² - 22x - 21= 0 are -¾ and 7/2.

b) Given quadratic equation is 3√5x² +25x +10√5= 0.

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 3√5 , b= 25, c= 10√5

Now,ac= 3√5 × 10√5= 30×5= 150

Here, c have +ve sign so we have to find the factors of  150  whose sum  is 25. Such factors 15 and 10.

3√5x² +25x +10√5= 0.

3√5x² +15x + 10x +10√5= 0.

3x(√5x + 5) + 2√5(√5x + 5)= 0

(3x +2√5) (√5x + 5) = 0

(3x +2√5) = 0   or  (√5x + 5) = 0

3x = -2√5     or √5x = -5

x = -2√5/3    or x = -5/ √5= -5×√5/√5×√5= -5√5/5= -√5  [by rationalising the denominator]

Hence, roots of equation 3√5x² +25x +10√5= 0 are -2√5/3 and -√5.

HOPE THIS WILL HELP you

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