MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Consider the quadratic equation (t2−4t+3)x2+6x+1=0, where t is a positive real parameter.
(i) State the condition on t that ensures the given equation remains quadratic in x.
(ii) Compute the discriminant in terms of t.
(iii) Using the discriminant, find the range of positive values of t for which the equation has real roots.