Quadratic Equation by Discussion
1. Use the discriminant to find out the count of the roots of following equations:
| x2–14x +33=0 | D=(-14)2-4.1.33=64 | Two different roots in real numbers |
| 4x2–5x+1=0 | D=(-5)2-4.4.1=9 | Two different roots in real numbers |
| x2–10x+25=0 | D=(-10)2-4.1.25=0 | One (double) root in real numbers |
| 12x2–5x-3=0 | D=(-5)2-4.12.(-3)=169 | Two different roots in real numbers |
| x2–4x+13=0 | D=(-4)2-4.1.13=–36 | No solution in real numbers |
| x2–14x+49=0 | D=(-14)2–4.1.49=0 | One (double) root in real numbers |
| x2–6x+25=0 | D=(-6)2-4.1.25=–64 | No solution in real numbers |
2. For which „m“ do the quadratic equations have one (double) real root?
D = 0
b2-4ac = 0
42-4.1.m = 0
4m = 16
m = 4
x2+4x+4=0
D = 0
b2–4ac = 0
(4m-2)2–4m(4m+1) = 0
16m2–16m+4–16m2–4m = 0
–20m = –4
m = 1/5
x2-6x+9 = 0
D = 0
b2–4ac = 0
(2m-2)2–4m(m+2) = 0
4m2-8m+4–4m2-8m = 0
–16m = –4
m = ¼
x2–6x+9 = 0
3. For which „k“ does the equation kx2+(2k+1)x+(k-1)=0 have two different roots in real numbers?
Please log in to view the solution.4. Find „k“ so that the equation x2 -5x +k = 0 wouldn‘t have a root in real numbers.
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Please log in to view the solution.6. Find all „a“, for which one of the equation‘s roots equals null. 2(a-1)x2–(2a-4)x+2a(a-3) = 0. Find out the second root.
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8.
For which „m“ does the equation mx2 +(4m –2)x +(4m+1) = 0 have one (double) root in real numbers?
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9.
For which parameters „a“ the equation‘s roots x2 – (3a+2)x + a2 = 0 fit the relation x1 = 9x2 ? Determine those roots!
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10.
For which parameters „a“ in equation 2x2 – (a+1)x+(a-1) = 0 fits x1 – x2 = x1 . x2 ?
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