Advertisements
Advertisements
प्रश्न
Solving the following quadratic equation by factorization method:
\[6 x^2 - 17ix - 12 = 0\]
उत्तर
\[ 6 x^2 - 17ix - 12 = 0\]
\[ \Rightarrow 6 x^2 - 9ix - 8ix - 12 = 0\]
\[ \Rightarrow 3x\left( 2x - 3i \right) - 4i\left( 2x - 3i \right) = 0\]
\[ \Rightarrow \left( 2x - 3i \right)\left( 3x - 4i \right) = 0\]
\[ \Rightarrow \left( 2x - 3i \right) = 0 or \left( 3x - 4i \right) = 0\]
\[ \Rightarrow x = \frac{3}{2}i, \frac{4}{3}i\]
\[\text { So, the roots of the given quadratic equation are } \frac{3}{2}i \text { and } \frac{4}{3}i . \]
APPEARS IN
संबंधित प्रश्न
Solve the equation x2 + 3 = 0
Solve the equation –x2 + x – 2 = 0
Solve the equation `sqrt2x^2 + x + sqrt2 = 0`
Solve the equation `3x^2 - 4x + 20/3 = 0`
If z1 = 2 – i, z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`
x2 + 2x + 5 = 0
\[x^2 - x + 1 = 0\]
\[17 x^2 - 8x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[17 x^2 + 28x + 12 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[13 x^2 + 7x + 1 = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + 10ix - 21 = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 2 + i \right) x - \left( 1 - 7i \right) = 0\]
Solve the following quadratic equation:
\[i x^2 - 4 x - 4i = 0\]
Solve the following quadratic equation:
\[2 x^2 + \sqrt{15}ix - i = 0\]
Solve the following quadratic equation:
\[x^2 - x + \left( 1 + i \right) = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Solve the following quadratic equation:
\[x^2 - \left( \sqrt{2} + i \right) x + \sqrt{2}i = 0\]
Write the number of real roots of the equation \[(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0\].
If roots α, β of the equation \[x^2 - px + 16 = 0\] satisfy the relation α2 + β2 = 9, then write the value P.
Write roots of the equation \[(a - b) x^2 + (b - c)x + (c - a) = 0\] .
The complete set of values of k, for which the quadratic equation \[x^2 - kx + k + 2 = 0\] has equal roots, consists of
For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is
If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to
The number of real roots of the equation \[( x^2 + 2x )^2 - (x + 1 )^2 - 55 = 0\] is
If x is real and \[k = \frac{x^2 - x + 1}{x^2 + x + 1}\], then
If the roots of \[x^2 - bx + c = 0\] are two consecutive integers, then b2 − 4 c 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 number of roots of the equation \[\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}\] is
If α, β are the roots of the equation \[x^2 + px + q = 0 \text { then } - \frac{1}{\alpha} + \frac{1}{\beta}\] are the roots of the equation
If the difference of the roots of \[x^2 - px + q = 0\] is unity, then
Find the value of a such that the sum of the squares of the roots of the equation x2 – (a – 2)x – (a + 1) = 0 is least.
If 1 – i, is a root of the equation x2 + ax + b = 0, where a, b ∈ R, then find the values of a and b.
