Question

write the equation that should be formed by squaring each root of the equation x²- 3x+2=0 ​

Answer 1

Answer:

(x+1)(x+2)

Step-by-step explanation:

x^2+ 2x+x +2

x( x+2) +(x+2)

(x+1)(x+2)

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Answer 2

Given : x² - 3x + 2 = 0

To Find : equation formed by squaring each root of the equation

Solution:

x² - 3x + 2 = 0

Method 1 : By finding roots

x² - 2x - x + 2 = 0

=> (x - 2)(x - 1) =0

2 & 1 are roots

equation formed by squaring each root of the equation

(x - 2²)(x - 1²) =0

=> (x - 4)(x - 1) = 0

=> x² - 5x + 4 = 0

Method 2 :

Without find roots

α , β are roots of x² - 3x + 2 = 0

α + β =  3   αβ  = 2

α² , β² are roots

x² - (α² + β²)x + α²β² = 0  is the Equation

α² + β² = (α + β )² - 2αβ = 3² - 2(2) = 9 - 4 = 5

α²β² = (αβ )²   = 2²  = 4  

x² - 5x +4 = 0  

x² - 5x +4 = 0   is   formed by squaring each root of the equation x²- 3x+2=0 ​

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