There are three ways to solve a quadratic equation.
ii) Quadratic formula
Here we are going to see, how to solve quadratic equation using quadratic formula.
General form of quadratic equation is
ax^{2} + bx + c = 0
Use the quadratic formula to solve exactly for x :
Problem 1 :
x^{2} - 4x - 3 = 0
Solution :
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 1, b = -4 and c = -3
b^{2} – 4ac = (-4)^{2} – 4 (1) (-3)
= 16 + 12
= 28
Problem 2 :
x^{2} + 6x + 7 = 0
Solution :
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 1, b = 6 and c = 7
b^{2} – 4ac = (6)^{2} – 4 (1) (7)
= 36 - 28
= 8
Problem 3 :
x^{2} + 1 = 4x
Solution :
x^{2} + 1 = 4x
x^{2} - 4x + 1 = 0
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 1, b = -4 and c = 1
b^{2} – 4ac = (-4)^{2} – 4 (1) (1)
= 16 - 4
= 12
Problem 4 :
x^{2} + 4x = 1
Solution :
x^{2} + 4x = 1
x^{2} + 4x – 1 = 0
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 1, b = 4 and c = -1
b^{2} – 4ac = (4)^{2} – 4 (1) (-1)
= 16 + 4
= 20
Problem 5 :
x^{2} – 4x + 2 = 0
Solution :
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 1, b = -4 and c = 2
b^{2} – 4ac = (-4)^{2} – 4 (1) (2)
= 16 - 8
= 8
Problem 6 :
2x^{2} – 2x – 3 = 0
Solution :
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 2, b = -2 and c = -3
b^{2} – 4ac = (-2)^{2} – 4 (2) (-3)
= 4 + 24
= 28
Problem 7 :
x^{2} – 2√2x + 2 = 0
Solution :
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 1, b = -2√2 and c = 2
b^{2} – 4ac = (-2√2)^{2} – 4 (1) (2)
= 8 - 8
= 0
Problem 8 :
(3x + 1)^{2} = -2x
Solution :
(3x + 1)^{2} = -2x
(3x)^{2} + 1^{2} + 2(3x)(1) = -2x
9x^{2} + 1 + 6x = -2x
9x^{2} + 6x + 2x + 1 = 0
9x^{2} + 8x + 1 = 0
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 9, b = 8 and c = 1
b^{2} – 4ac = (8)^{2} – 4 (9) (1)
= 64 - 36
= 28
Problem 9 :
(x + 3)(2x + 1) = 9
Solution :
(x + 3)(2x + 1) = 9
2x^{2} + x + 6x + 3 = 9
2x^{2} + 7x + 3 = 9
2x^{2} + 7x + 3 – 9 = 0
2x^{2} + 7x – 6 = 0
By comparing the given quadratic equation with general form of quadratic equation,
ax^{2} + bx + c = 0
a = 2, b = 7 and c = -6
b^{2} – 4ac = (7)^{2} – 4 (2) (-6)
= 49 + 48
= 97
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM