English

Solve the equation 27x2 – 10x + 1 = 0 - Mathematics

Advertisements
Advertisements

Question

Solve the equation 27x2 – 10x + 1 = 0

Sum

Solution

The given quadratic equation is 27x2 – 10x + 1 = 0

On comparing the given equation with ax2 + bx + c = 0, we obtain

a = 27, b = –10, and c = 1

Therefore, the discriminant of the given equation is

D = b2 – 4ac = (–10)2 – 4 × 27 × 1 = 100 – 108 = –8

Therefore, the required solutions are

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Complex Numbers and Quadratic Equations - Miscellaneous Exercise [Page 112]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Miscellaneous Exercise | Q 8 | Page 112

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Solve the equation x2 – x + 2 = 0


Solve the equation `x^2 + x + 1/sqrt2 = 0`


If z1 = 2 – i,  z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`


x2 + 1 = 0


9x2 + 4 = 0


4x2 − 12x + 25 = 0


\[x^2 + 2x + 5 = 0\]


\[17 x^2 - 8x + 1 = 0\]


\[13 x^2 + 7x + 1 = 0\]


\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]


\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]


\[x^2 + x + \frac{1}{\sqrt{2}} = 0\]


\[x^2 + \frac{x}{\sqrt{2}} + 1 = 0\]


Solving the following quadratic equation by factorization method:

\[6 x^2 - 17ix - 12 = 0\]

 

Solve the following quadratic equation:

\[x^2 - \left( 2 + i \right) x - \left( 1 - 7i \right) = 0\]


Solve the following quadratic equation:

\[x^2 + 4ix - 4 = 0\]


Solve the following quadratic equation:

\[2 x^2 + \sqrt{15}ix - i = 0\]


Solve the following quadratic equation:

\[2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0\]


Write the number of quadratic equations, with real roots, which do not change by squaring their roots.


If α, β are roots of the equation \[x^2 + lx + m = 0\] , write an equation whose roots are \[- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}\].


If a, b are the roots of the equation \[x^2 + x + 1 = 0, \text { then } a^2 + b^2 =\]


The values of x satisfying log3 \[( x^2 + 4x + 12) = 2\] are


If x is real and \[k = \frac{x^2 - x + 1}{x^2 + x + 1}\], then


If the equations \[x^2 + 2x + 3\lambda = 0 \text { and } 2 x^2 + 3x + 5\lambda = 0\]  have a non-zero common roots, then λ =


If one root of the equation \[x^2 + px + 12 = 0\] while the equation \[x^2 + px + q = 0\] has equal roots, the value of q is


The value of p and q (p ≠ 0, q ≠ 0) for which pq are the roots of the equation \[x^2 + px + q = 0\] are

 

The set of all values of m for which both the roots of the equation \[x^2 - (m + 1)x + m + 4 = 0\] are real and negative, is


The number of roots of the equation \[\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}\] is 


If α and β are the roots of \[4 x^2 + 3x + 7 = 0\], then the value of \[\frac{1}{\alpha} + \frac{1}{\beta}\] is


If the difference of the roots of \[x^2 - px + q = 0\]  is unity, then

 

The least value of which makes the roots of the equation  \[x^2 + 5x + k = 0\]  imaginary is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×