Consider the equation (k-1)x^2 + (k-1)x + 1 = 0 with k not equal to 1. For what range of k does it have real roots?

Question

Accepted Answer

k < 1 or k >= 5. Real roots need D >= 0: (k-1)^2 - 4(k-1)(1) >= 0, i.e. (k-1)(k-1-4) >= 0, so (k-1)(k-5) >= 0. This product is >= 0 when k <= 1 or k >= 5. Since k cannot equal 1 (else not quadratic), the range is k < 1 or k >= 5.

Consider the equation $(k - 1) x^{2} + (k - 1) x + 1 = 0$ with $k$ not equal to 1.
For what range of $k$ does it have real roots?

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More Class 10 Discriminant and Nature of Roots practice

Consider the equation (k−1)x2+(k−1)x+1=0 with k not equal to 1.For what range of k does it have real roots?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Discriminant and Nature of Roots practice

Consider the equation $(k - 1) x^{2} + (k - 1) x + 1 = 0$ with $k$ not equal to 1.
For what range of $k$ does it have real roots?