Solve the inequality 6x - 7 + x^2 > 0

Firstly rearrange the quadratic such that the coefficient of x2 is positive (already done in this example) and the quadratic is in the form of ax2 +bx + c, then solve for x, like you would solve a regular quadratic equation.
x2 + 6x - 7 > 0, (x + 7)(x - 1) > 0
This gives you the roots of this quadratic aka where the graph intersects the x axis. This is important as this tells you which values of x satisfy the inequality (would be best explained by drawing a quadratic graph). In this situation it is when the graph is above the x axis, so therefore be before the lowest root and after the highest root.
x = -7, x = +1
Therefore, x < -7, x > 1

Related Maths A Level answers

All answers ▸

How do you find the minimum of the equation sin^2(x) + 4sin(x)?


dy/dx= 2x/2 - 1/4x, what is d2y/dx2?


Use the binomial series to find the expansion of 1/(2+5x)^3 in ascending powers of x up to x^3 (|x|<2/5)


Integrate (2x)(e^x)dx