Question

2x^2+3x+3=0
Find its roots​

Answer 1

Step 1: Use the quadratic formula

$\sf \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a}$

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

2x² + 3x + 3 = 0

$\sf \: a = \color{purple}2$

$\sf \: b = \color{blue}3$

$\sf \: c = \color{red}3$

$\sf \: x = \frac{ - 3± \sqrt{ {3}^{2} - 4 \: . \: \color{purple}2 \: . \: \color{blue}3 } }{2 \: . \: \color{purple}2}$

Step 2: Simplify

• Evaluate the exponent

• Multiply the numbers

• Subtract the numbers

• Multiply the numbers

$\sf \: x = \frac{ - 3± \sqrt{ - 15} }{4}$

Step 3: No real solutions because the discriminant is negative

The square root of a negative number is not a real number

d = − 15

Result:

No solution