Question

solve 2xsquare+x+4=0 by applying quadraric formula​

Answer 1

Appropriate Question :-

Solve 2x² + x + 4 = 0 by applying quadratic formula.

Solution :-

According to the question,

First, now the general formula of quadratic equation is ax² + bx + c in the question the same equation is given which is 2x² + x + 4. But, here we apply to the equation the quadratic formula.

Now, let's know the Quadratic formula,

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

Now, the question is what is the a, b and c. a, c and c are in the general formula before finding the x we have to find the a, b and c. For find a, b and c we have to compare the given equation with ax² + bx + c.

On comparing the equation. We get,

➵ a = 2

➵ b = 1

➵ c = 4

Now, we substitute the all gotten values in Quadratic formula, then we get, the value of x.

$\sf:\longmapsto{x = \frac{ - (1)± \sqrt{(1) {}^{2} - 4(2)(4) } }{2(2)}}$

On opening all brackets we get,

$\sf:\longmapsto{x = \frac{ - 1± \sqrt{1 - 32} }{4}} \\ \\ \sf:\longmapsto{x = \frac{ - 1± \sqrt{ - 31} }{4}} \: \: \: \:$

Now, we got the value of x but is in the ± we have separate them.

On separating we get,

$\sf:\longmapsto{x = \frac{1 + \sqrt{ - 31} }{4}} \: \\ \\ \sf:\longmapsto{x = \frac{1 - \sqrt{ - 31} }{4}}$

Hence, the value of x is

$\small{\boxed{\rm{\longmapsto{x = \frac{1+\sqrt{-31}}{4} \: \: \: \: \: \: \: and \: \: \: \: \: \: \: x = \frac{1-\sqrt{-31}}{4} }}}}$

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac.

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