Q1
Answer
Given $x^2 + 2x - 7 = 0$, find the discriminant and hence state the number of real roots of the equation.
$32$, 2 roots
Q2
Answer
Given $x^2 + x + 3 = 0$, find the discriminant and hence state the number of real roots of the equation.
$-11$, 0 roots
Q3
Answer
Given $5x^2 + 8x + 3 = 0$, find the discriminant and hence state the number of real roots of the equation.
$4$, 2 roots
Q4
Answer
Given $3x^2 - 7x + 5 = 0$, find the discriminant and hence state the number of real roots of the equation.
$-11$, 0 roots
Q5
Answer
Given $4 - 11x + 8x^2 = 0$, find the discriminant and hence state the number of real roots of the equation.
$-7$, 0 roots
Q6
Answer
Given $x^2 + \frac{2}{3}x = \frac{1}{4}$, find the discriminant and hence state the number of real roots of the equation.
$\dfrac{13}{9}$, 2 roots
Q7
Answer
The equation $x^2 + x + k = 0$ has equal roots. Find the value of $k$.
$\dfrac{1}{4}$
Q8
Answer
The equation $x^2 + 2kx - k = 0$ has equal roots. Find the possible values of $k$.
$0, -1$
Q9
Answer
The equation $kx^2 - 2x + 3 = 2k$ has equal roots. Find the possible values of $k$.
$0.5, 1$
Q10
Answer
  1. Express $k^2 - 8k + 20$ in the form $(k+p)^2 + q$ where $p$ and $q$ are constants to be found.
  2. Hence prove that the equation $x^2 - kx + 2k = 5$ has two real roots for all values of $k$.
  1. $(k-4)^2 + 4$
  2. Discriminant is $k^2 - 8k + 20$ which has a minimum value of $4$ and is greater than zero for all values of $k$.