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# Solving a Quadratic Equation by Formula Method

The formula for finding roots of a quadratic equation a(x)2 + bx +c = 0 (derivation given in section 3.6.2) is x = (−b ± √[b2 − 4ac]) / 2a

Solving a Quadratic Equation by Formula Method

The formula for finding roots of a quadratic equation ax2 + bx +c = 0 (derivation given in section 3.6.2) is

### Example 3.33

Solve x2 + 2x 2 = 0 by formula method

### Solution

Compare x2 + 2x 2 = 0 with the standard form ax2 + bx +c = 0

a = 1, b = 2, c = -2

substituting the values of a, b and c in the formula we get,

Therefore, x = −1 + √3 ,  −1 − √3

### Example 3.34

Solve 2x2 − 3x − 3 = 0 by formula method.

### Solution

Compare 2x2  3x 3 = 0 with the standard form ax2 + bx + c = 0

substituting the values of a, b and c in the formula we get,

Example 3.35 Solve 3p2 + 2√5p – 5 = 0  by formula method

Solution

Solution Compare 3p2 + 2√5p – 5 = 0 with the Standard form ax2 + bx +c = 0

a = 3, b = 2√5, c = −5 .

p = (−b ± √[b2 − 4ac]) /  2a

substituting the values of a, b and c in the formula we get,

x = √5/3 , - √5

### Example 3.36

Solve pqx 2 ( p +q)2 x + ( p +q)2  = 0

Solution

Compare the coefficients of the given equation with the standard form ax 2 + bx +c = 0

a = pq , b = −(p +q)2 , c = ( p +q)2

substituting the values of a, b and c in the formula we get,

Tags : Example, Solution | Algebra , 10th Mathematics : UNIT 3 : Algebra
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10th Mathematics : UNIT 3 : Algebra : Solving a Quadratic Equation by Formula Method | Example, Solution | Algebra