Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
उत्तर
\[i x^2 - x + 12i = 0\]
\[ \Rightarrow i\left( x^2 + ix + 12 \right) = 0\]
\[ \Rightarrow x^2 + ix + 12 = 0\]
\[ \Rightarrow x^2 + 4ix - 3ix + 12 = 0\]
\[ \Rightarrow x\left( x + 4i \right) - 3i\left( x + 4i \right) = 0\]
\[ \Rightarrow \left( x + 4i \right)\left( x - 3i \right) = 0\]
\[ \Rightarrow \left( x + 4i \right) = 0 \text { or} \left( x - 3i \right) = 0\]
\[ \Rightarrow x = - 4i , 3i\]
\[\text { So, the roots of the given quadratic equation are - 4i and } 3i .\]
APPEARS IN
संबंधित प्रश्न
Solve the equation 2x2 + x + 1 = 0
Solve the equation –x2 + x – 2 = 0
Solve the equation `x^2 + x/sqrt2 + 1 = 0`
Solve the equation `3x^2 - 4x + 20/3 = 0`
Solve the equation `x^2 -2x + 3/2 = 0`
If z1 = 2 – i, z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`
9x2 + 4 = 0
\[x^2 + 2x + 5 = 0\]
\[5 x^2 - 6x + 2 = 0\]
\[x^2 - x + 1 = 0\]
\[17 x^2 - 8x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[2 x^2 + x + 1 = 0\]
\[\sqrt{2} x^2 + x + \sqrt{2} = 0\]
\[x^2 + \frac{x}{\sqrt{2}} + 1 = 0\]
\[x^2 - 2x + \frac{3}{2} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
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:
\[x^2 - x + \left( 1 + i \right) = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} - 2i \right) x - \sqrt{2} i = 0\]
Solve the following quadratic equation:
\[x^2 - \left( \sqrt{2} + i \right) x + \sqrt{2}i = 0\]
If \[2 + \sqrt{3}\] is root of the equation \[x^2 + px + q = 0\] than write the values of p and q.
If α, β are roots of the equation \[x^2 + lx + m = 0\] , write an equation whose roots are \[- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}\].
The complete set of values of k, for which the quadratic equation \[x^2 - kx + k + 2 = 0\] has equal roots, consists of
If a, b are the roots of the equation \[x^2 + x + 1 = 0, \text { then } a^2 + b^2 =\]
If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to
If α, β are the roots of the equation \[x^2 + px + 1 = 0; \gamma, \delta\] the roots of the equation \[x^2 + qx + 1 = 0, \text { then } (\alpha - \gamma)(\alpha + \delta)(\beta - \gamma)(\beta + \delta) =\]
If the roots of \[x^2 - bx + c = 0\] are two consecutive integers, then b2 − 4 c is
The value of a such that \[x^2 - 11x + a = 0 \text { and } x^2 - 14x + 2a = 0\] may have a common root is
The values of k for which the quadratic equation \[k x^2 + 1 = kx + 3x - 11 x^2\] has real and equal roots 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
The equation of the smallest degree with real coefficients having 1 + i as one of the roots is
