The quadratic formula questions with answers

Questions

1. Question 1x² + bx + c = 0

   Solve $x^{2} - 5x + 2 = 0$, giving your answers correct to 2 decimal places.

   Show the worked solution

   1. Step 1: Read off a, b and c$a = 1,\ b = -5,\ c = 2$
   2. Step 2: Substitute into the formula$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(2)}}{2(1)}$$x = \dfrac{5 \pm \sqrt{17}}{2}$
   3. Step 3: Work out both answers, then round$x = 4.5615\ldots$ or $x = 0.4384\ldots$$x = 4.56$ or $x = 0.44$ (2 d.p.)
2. Question 2ax² + bx + c = 0

   Solve $4x^{2} - 6x - 9 = 0$, giving your answers correct to 2 decimal places.

   Show the worked solution

   1. Step 1: Read off a, b and c$a = 4,\ b = -6,\ c = -9$
   2. Step 2: Substitute into the formula$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(4)(-9)}}{2(4)}$$x = \dfrac{6 \pm \sqrt{180}}{8}$
   3. Step 3: Work out both answers, then round$x = 2.4270\ldots$ or $x = -0.9270\ldots$$x = 2.43$ or $x = -0.93$ (2 d.p.)
3. Question 3Rearrange first

   Solve $x(2x + 9) = 2$, giving your answers correct to 2 decimal places.

   Show the worked solution

   1. Step 1: Expand the bracket$2x^{2} + 9x = 2$
   2. Step 2: Write it as ax² + bx + c = 0$2x^{2} + 9x - 2 = 0$
   3. Step 3: Read off a, b and c$a = 2,\ b = 9,\ c = -2$
   4. Step 4: Substitute into the formula$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$x = \dfrac{-9 \pm \sqrt{(9)^2 - 4(2)(-2)}}{2(2)}$$x = \dfrac{-9 \pm \sqrt{97}}{4}$
   5. Step 5: Work out both answers, then round$x = 0.2122\ldots$ or $x = -4.7122\ldots$$x = 0.21$ or $x = -4.71$ (2 d.p.)
4. Question 4Negative x² term, jumbled order

   Solve $4 -x -4x^{2} = 0$, giving your answers correct to 2 decimal places.

   Show the worked solution

   1. Step 1: Multiply by −1 and reorder$4x^{2} + x - 4 = 0$
   2. Step 2: Read off a, b and c$a = 4,\ b = 1,\ c = -4$
   3. Step 3: Substitute into the formula$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$x = \dfrac{-1 \pm \sqrt{(1)^2 - 4(4)(-4)}}{2(4)}$$x = \dfrac{-1 \pm \sqrt{65}}{8}$
   4. Step 4: Work out both answers, then round$x = 0.8827\ldots$ or $x = -1.1327\ldots$$x = 0.88$ or $x = -1.13$ (2 d.p.)