which of the following quadratic equations do not have real roots
Answers
Answer:
A quadratic equation, ax2 + bx + c = 0; a ≠ 0 will have two distinct real roots if its discriminant, D = b2 - 4ac > 0. Hence, the equation x2 –3x + 4 = 0 has no real roots. Hence, the equation 2x2 + x – 1 = 0 has two distinct real roots. Hence, the equation 3x2 – 4x + 1 = 0 has two distinct real roots.
Given : Quadratic Equations
To Find : Which of the following Quadratic equations do not have real roots?
A x² +4x+3√2 =0
B x² +4x-3 √2=0
C x²+5x+3√2=0
D 3 x² +4√3x+4=0
Solution:
ax² + bx + c = 0
roots are not real if D < 0
D = b² - 4ac
A x² +4x+3√2 =0
=> D = 4² - 4(3√2)
=> D = 16 - 16.97
=> D < 0
roots are not real
B x² +4x-3 √2=0
=> D = 4² - (4(-3√2))
=> D = 16 + 16.97
=> D> 0
roots are real
C x² +5x+3√2 =0
=> D = 5² - 4(3√2)
=> D = 25 - 16.97
=> D > 0
roots are real
D 3 x² +4√3x+4=0
=> D = (4√3)² - 4(3)(4)
=> D = 48 - 48
=> D = 0
roots are real and Equal
x² +4x+3√2 =0 does not have real roots
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