Advertisements
Advertisements
Question
Solving the following quadratic equation by factorization method:
\[x^2 + 10ix - 21 = 0\]
Solution
\[ x^2 + 10ix - 21 = 0\]
\[ \Rightarrow x^2 + 7ix + 3ix - 21 = 0\]
\[ \Rightarrow x\left( x + 7i \right) + 3i\left( x + 7i \right) = 0\]
\[ \Rightarrow \left( x + 7i \right)\left( x + 3i \right) = 0\]
\[ \Rightarrow \left( x + 7i \right) = 0 or \left( x + 3i \right) = 0\]
\[ \Rightarrow x = - 7i, - 3i\]
\[\text { So, the roots of the given quadratic equation are - 3i and - 7i } .\]
APPEARS IN
RELATED QUESTIONS
Solve the equation x2 + 3 = 0
Solve the equation x2 – x + 2 = 0
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2 – Imz1 Imz2
Solve the equation `x^2 -2x + 3/2 = 0`
Solve the equation 21x2 – 28x + 10 = 0
4x2 − 12x + 25 = 0
x2 + x + 1 = 0
\[x^2 - 4x + 7 = 0\]
\[21 x^2 - 28x + 10 = 0\]
\[2 x^2 + x + 1 = 0\]
\[- x^2 + x - 2 = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
Solving the following quadratic equation by factorization method:
\[6 x^2 - 17ix - 12 = 0\]
Solve the following quadratic equation:
\[i x^2 - 4 x - 4i = 0\]
Solve the following quadratic equation:
\[x^2 + 4ix - 4 = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} - 2i \right) x - \sqrt{2} i = 0\]
Write the number of real roots of the equation \[(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0\].
If the difference between the roots of the equation \[x^2 + ax + 8 = 0\] is 2, write the values of a.
Write roots of the equation \[(a - b) x^2 + (b - c)x + (c - a) = 0\] .
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
For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is
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
The number of real roots of the equation \[( x^2 + 2x )^2 - (x + 1 )^2 - 55 = 0\] is
If α, β are the roots of the equation \[a x^2 + bx + c = 0, \text { then } \frac{1}{a\alpha + b} + \frac{1}{a\beta + b} =\]
If α, β are the roots of the equation \[x^2 + px + 1 = 0; \gamma, \delta\] the roots of the equation \[x^2 + qx + 1 = 0, \text { then } (\alpha - \gamma)(\alpha + \delta)(\beta - \gamma)(\beta + \delta) =\]
The number of real solutions of \[\left| 2x - x^2 - 3 \right| = 1\] 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
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 p, q are the roots of the equation \[x^2 + px + q = 0\] are
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 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
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.
