Advertisements
Advertisements
Question
The number of roots of the equation \[\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}\] is
Options
0
1
2
3
Solution
1
\[\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{(x - 2)}{(x + 4)}\]
\[ \Rightarrow ( x^2 - 3x - 10) (x + 4) = ( x^2 + 3x - 18) (x - 2)\]
\[ \Rightarrow x^3 + 4 x^2 - 3 x^2 - 12x - 10x - 40 = x^3 - 2 x^2 + 3 x^2 - 6x - 18x + 36\]
\[ \Rightarrow x^2 - 22x - 40 = x^2 - 24x + 36\]
\[ \Rightarrow 2x = 76\]
\[ \Rightarrow x = 38\]
Hence, the equation has only 1 root.
APPEARS IN
RELATED QUESTIONS
Solve the equation x2 + 3 = 0
Solve the equation `sqrt3 x^2 - sqrt2x + 3sqrt3 = 0`
Solve the equation `x^2 + x/sqrt2 + 1 = 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 27x2 – 10x + 1 = 0
x2 + 1 = 0
\[x^2 - 4x + 7 = 0\]
\[x^2 - x + 1 = 0\]
\[x^2 + x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[17 x^2 + 28x + 12 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[13 x^2 + 7x + 1 = 0\]
\[x^2 + x + \frac{1}{\sqrt{2}} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + 10ix - 21 = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
Solve the following quadratic equation:
\[i x^2 - 4 x - 4i = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Write the number of real roots of the equation \[(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0\].
If a and b are roots of the equation \[x^2 - px + q = 0\], than write the value of \[\frac{1}{a} + \frac{1}{b}\].
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 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 solutions of `x^2 + |x - 1| = 1` is ______.
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
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 \[x^2 - p(x + 1) - c = 0, \text { then } (\alpha + 1)(\beta + 1) =\]
The equation of the smallest degree with real coefficients having 1 + i as one of the roots 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 ______.
