Advertisements
Advertisements
प्रश्न
\[x^2 - 4x + 7 = 0\]
उत्तर
We have:
\[x^2 - 4x + 7 = 0\]
\[ \Rightarrow x^2 - 4x + 4 + 3 = 0\]
\[ \Rightarrow x^2 - 2 \times x \times 2 + 2^2 - (\sqrt{3}i )^2 = 0\]
\[ \Rightarrow (x - 2 )^2 - (\sqrt{3}i )^2 = 0\]
\[ \Rightarrow (x - 2 + \sqrt{3}i) (x - 2 - \sqrt{3}i) = 0\]
\[\Rightarrow (x - 2 + \sqrt{3}i) = 0\] or, \[(x - 2 - \sqrt{3}i) = 0\]
\[\Rightarrow x = 2 - \sqrt{3}i\] or, \[x = 2 + \sqrt{3}i\]
Hence, the roots of the equation are \[2 \pm i\sqrt{3}\] .
APPEARS IN
संबंधित प्रश्न
Solve the equation x2 + 3 = 0
Solve the equation x2 + 3x + 5 = 0
If z1 = 2 – i, z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`
x2 + 1 = 0
x2 + 2x + 5 = 0
\[21 x^2 + 9x + 1 = 0\]
\[x^2 + x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[21 x^2 - 28x + 10 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[13 x^2 + 7x + 1 = 0\]
\[- x^2 + x - 2 = 0\]
\[x^2 - 2x + \frac{3}{2} = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + 10ix - 21 = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 - \left( 2\sqrt{3} + 3i \right) x + 6\sqrt{3}i = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2i} = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 2 + i \right) x - \left( 1 - 7i \right) = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
If roots α, β of the equation \[x^2 - px + 16 = 0\] satisfy the relation α2 + β2 = 9, then write the value P.
If α, β are roots of the equation \[x^2 + lx + m = 0\] , write an equation whose roots are \[- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}\].
For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is
The values of x satisfying log3 \[( x^2 + 4x + 12) = 2\] are
The number of solutions of `x^2 + |x - 1| = 1` 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
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 =
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
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 `|(z - 2)/(z + 2)| = pi/6`, then the locus of z is ______.
