Question

find the roots of quadratic equations if they exist
1.4x²+4√3x+3=0
2.5x²-7x-6=0
3.x²+5=-6x


pls ans fast

Answer 1

Hi ☺

4x²+4√3x + 3

= ( 2x )²+2.2x√3+ ( √3 )²

= ( 2x + √3 )²

either,

2x + √3 = 0

=> x = - √3/2

or x = -√3/2

roots are -√3/2 and -√3/2

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5x² - 7x - 6

= 5x² - ( 10 - 3 )x - 6

= 5x² - 10x + 3x - 6

= 5x ( x - 2 ) + 3 ( x - 2 )

= ( x - 2 ) ( 5x + 3 )

either

x - 2 = 0

=> x = 2

or

5x + 3 = 0

=> x = - 3/5

roots are -3/5 and 2

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x² + 5 = - 6x

= x² + 6x + 5

= x² + ( 5 + 1 )x + 5

= x² + 5x + x + 5

= x ( x + 5 ) + 1 ( x + 5 )

= ( x + 5 ) ( x + 1 )

either

x + 5 = 0

=> x = - 5

or

x + 1 = 0

=> x = -1

roots are -1 and -5

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