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

Chapter: 10th Mathematics : Algebra

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,



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