Review question

# Can we find the midpoint of a chord of this parabola? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8045

## Question

Given that $x_1$ and $x_2$ are the roots of $ax^2 + bx + c = 0$, state in terms of some or all of $a$, $b$, $c$: (i) the condition that $x_1 = x_2$, (ii) the value of $x_1 + x_2$.

1. Find the values of $m$ for which the line $y = mx$ is a tangent to the curve $y^2 = 3x - 1$.

2. The line $y = 2x$ meets the curve $3y = x^2 - 10$ at the points $A(x_1, y_1)$ and $B(x_2, y_2)$.
1. Obtain the quadratic equation whose roots are $x_1$ and $x_2$.
2. Without solving this equation, find the $x$ co-ordinate of the midpoint of $AB$.