Quadratic Irrational

An equation which consists of more than one terms are squared but no higher power in terms, having the syntax, ax2+bx+c where a represents the numerical coefficient of x2, b represents the numerical coefficient of x, and c represents the constant term

Example: 2x2+5x+20

The roots of the quadratic equation having the irrational number, such an equation is called quadratic irrational. In this content we shall discuss about quadratic irrational with suitable example problems.

Identify types of roots in quadratic equation:

A quadratic equation is in the form of ax2+bx+c,

First we need to find the discernment d = b2- 4ac

If d > 0, the roots are real roots and unequal

If d = 0, the roots are real and equal

If d < 0, the roots are irrational.

Example problem of quadratic irrational:

Solve the quadratic equation

x2+3x+5

Solution:

The equation is in the form of ax2+ bx +c

Where a = 1; b = 3; c = 5

Find the discernment d = b2- 4ac

d = (3)2 - 4* 1* 5

d = 9 -20

d = -11 < 0

If d < 0, the roots are irrational.

To Factor this expression we use quadratic formula method,

`x = ((-b)+-sqrt(b^2-4 * a*c)/(2*a))`

`x = (-3+-sqrt((3)^2-4*1*5))/(2*1)`

`x= (-3+-sqrt(9-20))/2`

`x = (-3+-sqrt(-11))/2`

`x= (-3+-i(3.31))/2` we know that `sqrt(-1) = i`

` x = (-3+-i3.31)/2 ` and `x = (-3-i3.31)/2`

Hence the answer is `x = (-3+-i3.31)/2` and `x = (-3-i3.31)/2`

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Example problem of quadratic irrational:

Solve the quadratic equation

x2+5x+9

Solution:

The equation is in the form of ax2+ bx +c

Where a = 1; b = 5; c = 9

Find the discernment d = b2- 4ac

d = (5)2 - 4* 1* 9

d = 25 -36

d = -11 < 0

If d < 0, the roots are irrational.

To Factor this expression we use quadratic formula method,

`x = ((-b)+-sqrt(b^2-4 * a*c)/(2*a))`

`x = (-5+-sqrt((5)^2-4*1*9))/(2*1)`

`x= (-5+-sqrt(25-36))/2`

`x = (-5+-sqrt(-11))/2`

`x= (-5+-i(3.31))/2` we know that `sqrt(-1) = i`

`x = (-5+-i3.31)/2` and `x = (-5-i3.31)/2`

Hence the answer is `x = (-5+-i3.31)/2` and `x = (-5-i3.31)/2`

Example problem of quadratic irrational:

Solve the quadratic equation

x2+7x+13

Solution:

The equation is in the form of ax2+ bx +c

Where a = 1; b = 7; c = 13

Find the discernment d = b2- 4ac

d = (7)2 - 4* 1* 13

d = 49 -52

d = -3 < 0

If d < 0, the roots are irrational.

To Factor this expression we use quadratic formula method,

`x = ((-b)+-sqrt(b^2-4 * a*c)/(2*a))`

`x = (-7+-sqrt((7)^2-4*1*13))/(2*1)`

`x= (-7+-sqrt(49-52))/2`

`x = (-7+-sqrt(-3))/2`

`x= (-7+-i(1.732))/2` we know that `sqrt(-1) = i`

`x = (-7+-i1.732)/2` and `x = (-7-i1.732)/2`

Hence the answer is `x = (-7+-i1.732)/2` and `x = (-7-i1.732)/2`

Example problem of quadratic irrational:

Solve the quadratic equation

x2+8x+17

Solution:

The equation is in the form of ax2+ bx +c

Where a = 1; b = 8; c = 17

Find the discernment d = b2- 4ac

d = (8)2 - 4* 1* 17

d = 64 -68

d = -4 < 0

If d < 0, the roots are irrational.

To Factor this expression we use quadratic formula method,

`x = ((-b)+-sqrt(b^2-4 * a*c)/(2*a))`

`x = (-8+-sqrt((8)^2-4*1*17))/(2*1)`

`x= (-8+-sqrt(64-68))/2`

` x = (-8+-sqrt(-4))/2`

`x= (-8+-i(2))/2` we know that `sqrt(-1) = i`

`x = (-8+-i2)/2` and `x = (-8-i2)/2`

Hence the answer is `x = (-8+-i2)/2` and `x = (-8-i2)/2`