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The roots of the equation 3x2 - 12x + 10 = 0 are?
- a)rational and unequal
- b)complex
- c)real and equal
- d)irrational and unequal
- e)rational and equal
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The roots of the equation 3x2- 12x + 10 = 0 are?a)rational and unequal...
The discriminant of the quadratic equation is (-12)2 - 4(3)(10) i.e., 24. As this is positive but not a perfect square, the roots are irrational and unequal.
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Most Upvoted Answer
The roots of the equation 3x2- 12x + 10 = 0 are?a)rational and unequal...
As D is positive
and should be rational and unequal
dint understand why it's ( d) where it should be(a)
and should be rational and unequal
dint understand why it's ( d) where it should be(a)
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Community Answer
The roots of the equation 3x2- 12x + 10 = 0 are?a)rational and unequal...
Solution:
Given equation is 3x^2 - 12x + 10 = 0.
We can find the nature of roots of the given quadratic equation using the discriminant.
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given as D = b^2 - 4ac.
If D > 0, then the roots are real and unequal.
If D = 0, then the roots are real and equal.
If D < 0,="" then="" the="" roots="" are="" />
In the given equation, a = 3, b = -12, and c = 10.
The discriminant is given as D = (-12)^2 - 4(3)(10) = 144 - 120 = 24.
Since D > 0, the roots are real and unequal.
However, the question asks for the type of roots in terms of their rationality. The roots of a quadratic equation can be rational or irrational.
If the roots are rational, then they can be expressed as a ratio of two integers.
If the roots are irrational, then they cannot be expressed as a ratio of two integers.
In this case, we can use the quadratic formula to find the roots of the given equation.
The quadratic formula is given as x = (-b ± √D) / 2a.
Substituting the values of a, b, c, and D, we get x = [12 ± √24] / 6.
Simplifying the roots, we get x = 2 ± √6.
Since √6 is an irrational number, the roots of the given equation are irrational and unequal.
Therefore, the correct option is (d) irrational and unequal.
Given equation is 3x^2 - 12x + 10 = 0.
We can find the nature of roots of the given quadratic equation using the discriminant.
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given as D = b^2 - 4ac.
If D > 0, then the roots are real and unequal.
If D = 0, then the roots are real and equal.
If D < 0,="" then="" the="" roots="" are="" />
In the given equation, a = 3, b = -12, and c = 10.
The discriminant is given as D = (-12)^2 - 4(3)(10) = 144 - 120 = 24.
Since D > 0, the roots are real and unequal.
However, the question asks for the type of roots in terms of their rationality. The roots of a quadratic equation can be rational or irrational.
If the roots are rational, then they can be expressed as a ratio of two integers.
If the roots are irrational, then they cannot be expressed as a ratio of two integers.
In this case, we can use the quadratic formula to find the roots of the given equation.
The quadratic formula is given as x = (-b ± √D) / 2a.
Substituting the values of a, b, c, and D, we get x = [12 ± √24] / 6.
Simplifying the roots, we get x = 2 ± √6.
Since √6 is an irrational number, the roots of the given equation are irrational and unequal.
Therefore, the correct option is (d) irrational and unequal.
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The roots of the equation 3x2- 12x + 10 = 0 are?a)rational and unequalb)complexc)real and equald)irrational and unequale)rational and equalCorrect answer is option 'D'. Can you explain this answer?
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