Question

write standard form of quardratic equation and find the root of the equation 3x²+5√2x+2=0 using general formula.​

Answer 1

Standard form of Quadratic equation : ax^2 + bx + c = 0

Here, a, b, c are real numbers and a is not equal to 0.

Given question : Find the roots of the equation 3x²+5√2x+2=0 using general formula.

Comparing the given equation with

ax^2 + bx + c = 0, we get :

a = 3

b = 5√2

c = 2

$\tt \small{ {b}^{2} - 4ac = (5 \sqrt{2}){}^{2} - 4 \times 3 \times 2}$

$\tt{ =( 25 \times 2) - 24 }$

$\tt{ = 50 - 24}$

$\tt{ = 26}$

Now, Using Formula Method,

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

$\tt{= \frac{ - 5 \sqrt{2}± \sqrt{26} }{6}}$

$\tt{= \frac{ - 5 \sqrt{2} + \sqrt{26} }{6}} \: \: or \: \: \tt{= \frac{ - 5 \sqrt{2} - \sqrt{26} }{6}}$

Thus,
Value of x is : $\tt{= \frac{ - 5 \sqrt{2} + \sqrt{26} }{6}} \: \: or \: \: \tt{= \frac{ - 5 \sqrt{2} - \sqrt{26} }{6}}$