Question

Use the quadratic formula to solve this probelm

-3x^2 - 24x -48=0
6x^2 + 5x + 2= 0
4x ^2+8x+3=0

Answer 1

(a)

`x=-4`

(b)

`x=-(5)/(12)+i(√(23))/(12),\:x=-(5)/(12)-i(√(23))/(12)`

(c)

`x=-(1)/(2),\:x=-(3)/(2)`

Explanation:

(a)

`-3x^2 - 24x -48=0`

we can compare it with standard quadratic equation

`ax^2+bx+c=0`

we can find a, b and c

`a=-3,b=-24,c=-48`

now, we can use quadratic formula

`x=(-b\pm √(b^2-4ac))/(2a)`

we can plug values

and we get

`x=(-\left(-24\right)\pm √(\left(-24\right)^2-4\left(-3\right)\left(-48\right)))/(2\left(-3\right))`

and we get

`x=-4`

(b)

`6x^2+5x+2=0`

we can compare it with standard quadratic equation

`ax^2+bx+c=0`

we can find a, b and c

`a=6,b=5,c=2`

now, we can use quadratic formula

`x=(-b\pm √(b^2-4ac))/(2a)`

we can plug values

`x=(-5\pm √(5^2-4\cdot \:6\cdot \:2))/(2\cdot \:6)`

we get

`x=-(5)/(12)+i(√(23))/(12),\:x=-(5)/(12)-i(√(23))/(12)`

(c)

`4x^2+8x+3=0`

we can compare it with standard quadratic equation

`ax^2+bx+c=0`

we can find a, b and c

`a=4,b=8,c=3`

now, we can use quadratic formula

`x=(-b\pm √(b^2-4ac))/(2a)`

we can plug values

`x=(-8\pm √(8^2-4\cdot \:4\cdot \:3))/(2\cdot \:4)`

we get

`x=-(1)/(2),\:x=-(3)/(2)`