For what values of does the equation have no real roots?

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For what values of tt does the equation x2−4tx+(t+5)=0x^{2} - 4tx + (t + 5) = 0 have no real roots? (a) −1≤t≤54-1 \le t \le \dfrac{5}{4} (b) t<−1 or t>54t < -1 \text{ or } t > \dfrac{5}{4} (c) −1<t<54-1 < t < \dfrac{5}{4} (d) t=−1 or t=54t = -1 \text{ or } t = \dfrac{5}{4}

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