IB Maths AA SL AA 2.2 practice question

Paper 2, calculatorMedium7 marks

For real $t$ let $q_t$ be the quadratic function defined by

q_t(x)=x^2+(t-4)x+2t+1.

(a)

Determine the discriminant, $\Delta_t$ of $q_t(x)$

[2]

(b)

Given that $0\leq t\leq 10$ determine the set of values of $t$ for which $q_t(x)=0$ has two distinct real roots.

[3]

(c)

Hence, identify the integer value of $t$ in this set and solve $q_t(x)\leq 0$ for $x\in\mathbb{R}$

[2]