Solving Quadratic Equations by the Quadratic Formula

Method of taking square roots In fact, for quadratic equations in the form (x + m)2 = n, we can solve them by taking square roots. We have learnt how to solve quadratic equations ax2 + bx + c = 0 by the factor method. e.g. (x – 3)2 = 16

Follow-up question How to solve (x + 5)2 = –9? (x + 5)2 = –9 ∴ The equation has no real roots. is not a real number. Follow-up question Solve (x + 1)2 = 25 by taking square roots. (x + 1)2 = 25

Yes. There is a formula which can solve all quadratic equations. x2 + 3x – 2 cannot be factorized by cross-method. Is there any way to solve x2 + 3x – 2 = 0? Yes. There is a formula which can solve all quadratic equations.

Rewrite the equation in the form (x + m)2 = n. ax2 + bx + c = 0 , where a  0 Step 1 Rewrite the equation in the form (x + m)2 = n. Divide both sides by a. Add the term to both sides. 2 ç è æ a b

Step 2 Take square roots on both sides. Step 3 Express the roots in terms of a, b and c. Quadratic formula

Using the quadratic formula Now, I can solve x2 + 3x – 2 = 0. a = 1 c = –2 ∴ b = 3

Solve 2x2  4x + 3 = 0 using the quadratic formula. Follow-up question Solve 2x2  4x + 3 = 0 using the quadratic formula.  Substitute a = 2, b = –4 and c = 3 into the formula. ∵ is not a real number. ∴ The equation has no real roots.