A quadratic equation in the form ax2+bx+c=0 can be solved using the quadratic formula. Sometimes, it is necessary to use the quadratic formula to solve a quadratic rather than factorising, as not all quadratics can be factorised easily.
The quadratic formula
The quadratic formula is
x=2a−b±b2−4ac
Where a,b and c are the co-efficients from the quadratic equation in the form
ax2+bx+c=0
Substitute the values of a,b and c from the quadratic equation into the quadratic formula, and calculate the solutions for x.
Example 1
Use the quadratic formula to solve
2x2+7x+3=0
From the quadratic equation,a=2,b=7andc=3. Substitute the numbers into the quadratic formula.
x=2a−b±b2−4ac
x=2×2−7±72−4×2×3
Work out the value inside the square root.
x=4−7±25
x=4−7±5
The± symbol means you have to do plus or minus, so there will be two calculations