Quadratic Functions (Cambridge (CIE) O Level Additional Maths): Exam Questions

Find the values of the constant $k$ for which the equation $(2k–1)x^2+6x+k+1=0$ has real roots.

Find the values of $x$ for which $12x^2-20x+5<\left(2x+1\right)\left(x-1\right)$.

Write $9x^2-12x+5$ in the form $p{(x-q)}^2+r$, where $p$,$q$ and $r$ are constants.

Hence write down the coordinates of the minimum point of the curve $y=9x^2-12x+5$.

Solve $2x^{\frac{2}{3}}-x^{\frac{1}{3}}-10=0$.

Find the set of values of $k$ for which $4x^2-4kx+2k+3=0$ has no real roots.

Solve $6x^{\frac{2}{3}}-5x^{\frac{1}{3}}+1=0$.

Find the values of $k$ for which the line $y=kx+3$ is a tangent to the curve $y=2x^2+4x+k-1$.

Find the values of $k$ for which the line $y=x-3$ intersects the curve $y=k^2{x}^2+5kx+1$ at two distinct points.

Find the exact values of the constant $k$ for which the line $y=2x+1$ is a tangent to the curve $y=4x^2+kx+k-2.$

Find the values of $k$ for which the line $y=kx-7$ and the curve $y=3x^2+8x+5$ do not intersect.

The curve $y=2x^2+k+4$ intersects the straight line $y=(k+4)x$ at two distinct points. Find the possible values of $k$.