Write the discriminant of the following quadratic equations:
(i) 2x²-5x+3=0
(ii) x²+2x+4=0
(iii) (x-1)(2x-1)=0
(iv) x²-2x+k=0,k=R
(v) √3x²+2√2x-2√3=0
(vi)x²-x+1=0
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Discriminant D = b² - 4ac for a Quadratic Equation ax² + bx + c = 0
Step-by-step explanation:
for a Quadratic Equation
ax² + bx + c = 0
Discriminant D = b² - 4ac
(i) 2x² - 5x + 3=0
D = (-5)² - 4(2)(3)
=> D = 25 - 24
=> D = 21
(ii) x² + 2x + 4=0
D = (2)² - 4(1)(4)
=> D = 4 - 16
=> D = -12
(iii) (x-1)(2x-1)=0
=> 2x² - 3x + 1 = 0
D = (-3)² - 4(2)(1)
=> D = 9 - 8
=> D = 1
(iv) x²-2x+k=0
D = (-2)² - 4(1)(k)
=> D = 4 - 4k
=> D = 4(1 - k)
(v) √3x²+2√2x-2√3=0
D = (2√2)² - 4(√3)(-2√3)
=> D = 8 + 24
=> D = 32
(vi) x² - x + 1 = 0
D = (-1)² - 4(1)(1)
=> D = 1 - 4
=> D = -3
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