Question

Solve the following quadratic equation:
$ {x^2} - \dfrac{{3x}}{{10}} - \dfrac{1}{{10}} = 0$ .

Answer 1

Hint: Quadratic equations are the equations having degree ‘2’. We can solve the equation by different methods. In this question the equation is not in standard form we need to convert it into the standard form which goes as $ a{x^2} + bx + c = 0$


Complete step-by-step solution:
The given equation is
$ {x^2} - \dfrac{{3x}}{{10}} - \dfrac{1}{{10}} = 0$
As we can see it is not in standard form and 10 is in denominator,
Multiplying both sides by 10 we get,
$ 10{x^2} - 3x - 1 = 0$
We can solve the given equation by factorization method as,
-3x can be written as -5x+2x
Which if multiplied gives product of a and c.
$
  10{x^2} - 3x - 1 = 0 \\
   \Rightarrow 10{x^2} - 5x + 2x - 1 = 0 \\
   \Rightarrow 5x(2x - 1) + 1(2x - 1) = 0 \\
 $
By taking the common factor,
$
   \Rightarrow (5x + 1)(2x - 1) = 0 \\
   \Rightarrow x = \dfrac{{ - 1}}{5},\dfrac{1}{2} \\
 $

Note: D is the discriminant of the quadratic equation given by $ D = \sqrt {({b^2} - 4ac)} $
If, D=0 the equation will have equal real roots.
If the D>0 equation will have distinct real roots.
If D<0 the roots will be imaginary.