There, We presented the Derivation Of Quadratic Formula in a lucid way. An Example in applying the formula is given. Another problem for practice is also given.

Here we present some more Solved Examples.

We also give problems for practice in Exercise.

Example 1 : Quadratic Formula Solver

Solve the following equation using Quadratic Formula

3x^{2} + 2x - 8 = 0

To solve 3x^{2} + 2x - 8 = 0 using Quadratic Formula Comparing this equation with ax^{2} + bx + c = 0, we get a = 3, b = 2 and c = -8 We know by Quadratic Formula, x = {(-b) ± √(b^{2} - 4ac)}⁄2a Applying this Quadratic Formula here, we get x = {(-b) ± √(b^{2} - 4ac)}⁄2a = [ (-2) ± √{(2)^{2} - 4(3)(-8)}]⁄2(3) = [ (-2) ± √{4 + 96}]⁄6 = [ (-2) ± √{100}]⁄6 = [(-2) ± 10]⁄6 = (-2 + 10)⁄6, (-2 - 10)⁄6 = 8⁄6, -12⁄6 = 4⁄3, -2 Ans.
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Example 2 : Quadratic Formula Solver

Solve the following equation using Quadratic Formula

8 - 5x^{2} - 6x = 0

To solve 8 - 5x^{2} - 6x = 0 using Quadratic Formula Multiplying the given equation by -1, we get 5x^{2} + 6x - 8 = 0 x -1 = 0 Comparing this equation with ax^{2} + bx + c = 0, we get a = 5, b = 6 and c = -8 We know by Quadratic Formula, x = {(-b) ± √(b^{2} - 4ac)}⁄2a Applying this Quadratic Formula here, we get x = {(-b) ± √(b^{2} - 4ac)}⁄2a = [ (-6) ± √{(6)^{2} - 4(5)(-8)}]⁄2(5) = [ (-6) ± √{36 + 160}]⁄10 = [ (-6) ± √{196}]⁄10 = [(-6) ± 14]⁄10 = (-6 + 14)⁄10, (-6 - 14)⁄10 = 8⁄10, -20⁄10 = 4⁄5, -2 Ans.

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Solve the following equation using Quadratic Formula

6x^{2} - 13x - 63 = 0

To solve 6x^{2} - 13x - 63 = 0 using Quadratic Formula Comparing this equation with ax^{2} + bx + c = 0, we get a = 6, b = -13 and c = -63 We know by Quadratic Formula, x = {(-b) ± √(b^{2} - 4ac)}⁄2a Applying this Quadratic Formula here, we get x = {(-b) ± √(b^{2} - 4ac)}⁄2a = [ -(-13) ± √{(-13)^{2} - 4(6)(-63)}]⁄2(6) = [ (+13) ± √{169 + 1512}]⁄12 = [ (13) ± √{1681}]⁄12 = [(13) ± 41]⁄12 = (13 + 41)⁄12, (13 - 41)⁄12 = 54⁄12, -28⁄12 = 9⁄2, -7⁄3 Ans.

Example 4 : Quadratic Formula Solver

Solved Example 4 on Quadratic Formula Solver :

Solve the following equation using Quadratic Formula √(x + 1) + √(x - 2) = √(x + 3)

Solution of Example 4 of Quadratic Formula Solver :

The given equation is √(x + 1) + √(x - 2) = √(x + 3) Squaring both sides, we get {√(x + 1) + √(x - 2)}^{2} = {√(x + 3)}^{2} ⇒ {√(x + 1)}^{2} + {√(x - 2)}^{2} + 2{√(x + 1)}{√(x - 2)} = (x + 3)

⇒ (2x - 1) - (x + 3) = -2[√{(x + 1)(x - 2)] ⇒ 2x - 1 - x - 3 = -2[√{(x + 1)(x - 2)] ⇒ x - 4 = -2[√{(x + 1)(x - 2)] Squaring both sides, we get (x - 4)^{2} = 4(x + 1)(x - 2) ⇒ x^{2} - 8x + 16 = 4(x^{2} - x - 2) = 4x^{2} - 4x - 8 ⇒ x^{2} - 4x^{2} - 8x + 4x + 16 + 8 = 0 ⇒ -3x^{2} - 4x + 24 = 0 ⇒ 3x^{2} + 4x - 24 = 0 Comparing this equation with ax^{2} + bx + c = 0, we get a = 3, b = 4 and c = -24 We know by Quadratic Formula, x = {(-b) ± √(b^{2} - 4ac)}⁄2a Applying this Quadratic Formula here, we get x = {(-b) ± √(b^{2} - 4ac)}⁄2a = [ -(4) ± √{(4)^{2} - 4(3)(-24)}]⁄2(3) = [ (-4) ± √{16 + 288}]⁄6 = [-4 ± √(304)]⁄6 = [-4 ± √{4(76)}]⁄6 = [-4 ± 2{√(76)}]⁄6 = [-2 ± {√(76)}]⁄3. Ans.

Exercise : Quadratic Formula Solver

Problems on Quadratic Formula Solver :

Solve the following equations using Quadratic Formula

x^{2} + 16x + 48 = 0

10x^{2} - 7x - 12 = 0

16x - 15 - 4x^{2} = 0

Solve the following equations using Quadratic Formula √(x + 8) - √(x + 3) = √x

For Answers See at the bottom of the Page.

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