Question

√2x^2 - 3x + √2 = 0​

Answer 1

Step-by-step explanation:

SOLUTION :  

Given :√2x² - 3x - 2√2 = 0

√2x² - 4x + x - 2√2 = 0

[ 4 × 1 = 4 & - 4 +1 = - 3]

√2x(x - 2√2) + 1(x - 2√2) = 0

(√2x + 1) (x - 2√2) = 0

√2x + 1 = 0   or  x - 2√2 = 0  

√2x = - 1  or  x = 2√2

x =  - 1/√2  or  x = 2√2

Hence, √2x² - 3x - 2√2 = 0

are - 1/√2  &  2√2 .

★★ METHOD TO FIND SOLUTION OF a quadratic equation by

FACTORIZATION METHOD :  

We first write the given quadratic polynomial as product of two linear factors by splitting the middle term and then equate each factor to zero to get desired roots of given quadratic equations

Answer 2

Concept

The formula to calculate the square root of a polynomial is given as, suppose the polynomial is ax^2+bx+c, then the formula for the roots will be

x=(-b+sqrt(b^2-4ac))/(2a) and x=(-b-sqrt(b^2-4ac))/(2a)

Since the polynomial is quadratic, therefore there will be two roots.

Given

The given polynomial is,

√2x^2 - 3x + √2 = 0​

Therefore, a=√2, b=-3 and c=√2.

Find

We have to calculate the roots of the given polynomials.

Solution

Since, the given data is as follows a=√2, b=-3 and c=√2, therefore substituting these values into the given formula to calculate the two values of the roots.

x=(-b+sqrt(b^2-4ac))/(2a)  and  x=(-b-sqrt(b^2-4ac))/(2a)

x=(3+sqrt(9- 4*2))/(2*√2) and x=x=(3-sqrt(9- 4*2))/(2*√2)

x=(3+sqrt(9- 8))/(2*√2) and x=(3-sqrt(9- 8))/(2*√2)

x=(3+1)/(2√2) and x=(3-1)/(2√2)

x=2/√2 and x=1/√2

x=√2 and x=1/√2

Hence the values of the two roots of the given polynomial are √2 and 1/√2.

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