The equation of a curve is $y=3{{x}^{2}}-kx+k$, where $k$ is a constant. Find the smallest value

Question

The equation of a curve is $y=3{{x}^{2}}-kx+k$, where $k$ is a constant. Find the smallest value of the integer $k$ for which the curve is always positive for all values of $x$. Find the set of values of $k$ for which the line $y=2x-2$ intersects the curve at two distinct points.

Accepted Answer

(a) $k=1$ (b) $k10$

Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

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