SOLVING QUADRATIC EQUATION BY USING QUADRATIC FORMULA WORKSHEET
About "Solving quadratic equation by using quadratic formula worksheet"
Solving quadratic equation by using quadratic formula worksheet :
Here we are going to see some practice questions on solving quadratic equation by using quadratic formula.
Solving quadratic equation by using quadratic formula worksheet - Practice 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 - Solution
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
|
= -b ± √ (b2- 4ac)/2a = -(-2) ± √(4-(-96))/2(1) = 2 ± √(4+96)/2 = (2 ± √100)/2 = (2 ± √(10 x 10))/2 = (2 ± 10)/2 |
b2 = (-2)2 ==> 4 4ac = 4(1)(-24) = -96 |
|
= (2 + 10)/2 = 12/2 = 6 |
= (2 - 10)/2 = -8/2 = -4 |
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
|
a = 1 b = -2 c = -15 = -b ± √ (b2- 4ac)/2a b2- 4ac = 4-(-60) = 4 + 60 = 64 = -(-2) ± √64/2(1) = (2 ± 8)/2 |
b2 = (-2)2 ==> 4 4ac = 4(1)(-15) = -60 |
|
= (2 + 8)/2 = 10/2 = 5 |
= (2 - 8)/2 = -4/2 = -2 |
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
|
= -b ± √ (b2- 4ac)/2a b2-4ac = 81 - (-688) = 81 + 688 b2-4ac = 769 = -(-9) ± √769/2(1) = -(-9) ± √769/2(1) = (9 ± √769)/2 |
b2 = (-9)2 = 81 4ac= 4(4)(-43) = -688 |
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