Consider the following two statements: Statement (I): (x2 + 3x + 1) = (x - 2)2 is not a quadratic equation. Statement (II): The nature of roots of quadratic equations x2 + 2x√3 + 3 = 0 are real and…
Question and options
Consider the following two statements:
Statement (I): (x2 + 3x + 1) = (x - 2)2 is not a quadratic equation.
Statement (II): The nature of roots of quadratic equations x2 + 2x√3 + 3 = 0 are real and equal.
In light of the given statements, choose the most appropriate answer from the given options.
- Both Statement I and Statement II are true.
- Both Statement I and Statement II are false.
- Statement I is true but Statement II is false.
- Statement I is false but Statement II is true.
Answer and explanation
Correct answer: A - Both Statement I and Statement II are true.
(I) x^2+3x+1 = x^2-4x+4 reduces to 7x-3 = 0, which is linear, so it is not a quadratic: true. (II) The discriminant is (2sqrt3)^2 - 4*3 = 0, so the roots are real and equal: true.
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