Learning Task 2. Complete the table
Answers
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
Learn More:
if alpha +beta are the roots of equation 4x²-5x+2=0 find the equation ..
brainly.in/question/8333453
obtain all the zeros of the polynomial 8x^4+8x^3-18x^2-20x-5 if two ...
brainly.in/question/7286826
If two zeroes of a polynomial p(x) = x4 – 5x3 – x2 + 35x – 42 are 2 and
brainly.in/question/17304050