SOLVING QUADRATIC EQUATION BY USING QUADRATIC FORMULA WORKSHEET

Solving Quadratic Equation by Using Quadratic Formula Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice solving quadratic equations using quadratic formula. 

Solving Quadratic Equation by Using Quadratic Formula Worksheet - Questions

Solving quadratic equation by using quadratic formula worksheet

(1)  x² - 2x - 24 = 0

(2)  x² - 2x - 15  =  0

(3)   x + (1/x) = 2 ½

(4)  3 a²x² - ab x - 2b² = 0   

(5)  a (x² + 1) =  x(a² + 1)

(6)  [(x - 1)/(x + 1)] + [(x - 3)/(x - 4)] = 10/3

Solving Quadratic Equation by Using Quadratic Formula Worksheet - Solutions

Question 1 :

Solve the following quadratic equations using quadratic formula 

 x² - 2x - 24 = 0

Solution :

By comparing the above equation with the general form of a quadratic equation ax² + bx + c = 0, we get

a = 1     b = -2    c = -24

Hence the solutions are 6 and -4.

Question 2 :

Solve the following quadratic equations using quadratic formula 

x² - 2x - 15  =  0

Solution :

By comparing the above equation with the general form of a quadratic equation ax² + bx + c = 0, we get

Hence the solutions are 5 and -2.

Question 3 :

Solve the following quadratic equations using quadratic formula 

 x + (1/x) = 2 ½

Solution :

(x² + 1)/x = 5/2

2 (x² + 1) = 5 x

2 x² + 2 = 5 x 

2 x² - 5 x + 2 = 0

By comparing the above equation with the general form of a quadratic equation ax² + bx + c = 0, we get

 x = 8/4 , 2/4

 x = 2 , 1/2

Hence the solutions are 2 and 1/2

Question 4 :

Solve the following quadratic equations using quadratic formula 

3 a²x² - ab x - 2b² = 0   

Solution :

By comparing the above equation with the general form of a quadratic equation ax² + bx + c = 0, we get

a = 3 a²   b = - ab   c = - 2b²

x = 6ab/6a²  , -4ab/6a²

x = b/a , x = -2b/a

Hence the solutions are b/a and -2b/a

Question 5 :

Solve the following quadratic equations using quadratic formula 

a (x² + 1) =  x(a² + 1)

Solution :

a x² + a =  x(a² + 1)

a x² - x(a² + 1) + a = 0

By comparing the above equation with the general form of a quadratic equation ax² + bx + c = 0, we get

a = a     b = -(a² + 1)   c = a    

        x = 2a²/2a , 2/2a

           = a , 1/a 

Hence the solutions are a and 1/a.

Question 6 :

Solve the following quadratic equations using quadratic formula 

 [(x - 1)/(x + 1)] + [(x - 3)/(x - 4)] = 10/3

Solution :

[(x - 1)(x - 4) + (x - 3)(x + 1)]/(x + 1)(x- 4) = 10/3

(x - 1)(x - 4)  =  x² - 5 x + 4  ---(1)

(x - 3)(x + 1)  =  x² - 2 x - 3  -----(2)

(x + 1)(x- 4)  =  (x² - 3 x - 4) -----(3)

(1) + (2) ==>x²-5x+4+x²-2x-3 = 2x²-7x+1  -----(4)

(4)/(3)  ==>  (2x²-7x+1)/(x² - 3 x - 4)  =  10/3

3 (2x² - 7 x + 1) = 10(x² - 3 x - 4)

10 x² - 6 x² - 30 x + 21 x - 40 - 3 = 0

4 x² - 9 x - 43 = 0

By comparing the above equation with the general form of a quadratic equation ax² + bx + c = 0, we get

a = 4     b = -9    c = -43

After having gone through the stuff given above, we hope that the students would have understood how to solve quadratic equations using quadratic formula. 

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