The equation (x^2-2(2t-1)x+(t^2+2)=0) has no real roots. Choose the correct interval for (t).

Here (D=4(2t-1)^2-4(t^2+2)=4(3t^2-4t-1)). From (D<0), the interval between the two boundary roots is obtained.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.

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Answer and explanation

Correct answer: (\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3})

Here (D=4(2t-1)^2-4(t^2+2)=4(3t^2-4t-1)). From (D<0), the interval between the two boundary roots is obtained.

What is the correct answer to this question?

(\frac{4-2\sqrt{6}}{3}<t<\frac{4+2\sqrt{6}}{3})

Why is this the correct answer?

Here (D=4(2t-1)^2-4(t^2+2)=4(3t^2-4t-1)). From (D<0), the interval between the two boundary roots is obtained.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.

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