Math, asked by AaronGregas, 15 days ago

Learning Task 2. Complete the table​

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Answers

Answered by amitnrw
0

Given : Quadratic Equations

x² - 6x - 27 = 0

x² - 25 = 0

x² + 10x + 25 = 0

2x² - 5x + 3 = 0

To Find : a , b , c

Discriminant

Nature of roots

Solution:

Quadratic Equation

ax² + bx + c = 0  ,  a≠0

D = discriminant =  b² - 4ac

D = 0  Equal and real roots

D > 0  Distinct real root

D < 0  roots are imaginary

x² - 6x - 27 = 0

a = 1 , b = - 6  , c = - 27

D = (-6)² - (4)(1)(-27) = 36 + 108 = 144

D > 0

Distinct real root

x² - 6x - 27 = 0 = (x - 9)(x + 3) = 0

roots are 9 , - 3

x² - 25 = 0

a = 1 , b = 0  , c = - 26

D = (0)² - (4)(1)(-25) = 100

D > 0

Distinct real root

roots are ±5

x² + 10x + 25 = 0

a = 1 , b =10  , c = 25

D = (10)² - (4)(1)(25) = 0

D = 0

Equal real root

x² + 10x + 25 = 0 => (x + 5)² = 0

Equal roots are -5 , - 5

2x² - 5x + 3 = 0

a=2 , b = - 5 , c = 3

D = 1

D>0

Distinct real root

2x² - 5x + 3 = 0

=> 2x² -2x -3x + 3 = 0

=> 2x(x - 1) - 3(x - 1) = 0

. x = 3/2  , x = 1

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