Advertisements
Advertisements
प्रश्न
The values of k for which the quadratic equation \[k x^2 + 1 = kx + 3x - 11 x^2\] has real and equal roots are
पर्याय
−11, −3
5, 7
5, −7
none of these
उत्तर
5, −7
The given equation is \[k x^2 + 1 = kx + 3x - 11 x^2\] which can be written as.
\[k x^2 + 11 x^2 - kx - 3x + 1 = \]
\[ \Rightarrow \left( k + 11 \right) x^2 - \left( k + 3 \right)x + 1 = 0\]
For equal and real roots, the discriminant of
\[\therefore \left( k + 3 \right)^2 - 4\left( k + 11 \right) = 0\]
\[ \Rightarrow k^2 + 2k - 35 = 0\]
\[ \Rightarrow \left( k - 5 \right)\left( k + 7 \right) = 0\]
\[ \Rightarrow k = 5, - 7\]
Hence, the equation has real and equal roots when \[k = 5 , - 7 .\]
APPEARS IN
संबंधित प्रश्न
Solve the equation `sqrt2x^2 + x + sqrt2 = 0`
Solve the equation `sqrt3 x^2 - sqrt2x + 3sqrt3 = 0`
Solve the equation `x^2 + x + 1/sqrt2 = 0`
Solve the equation `3x^2 - 4x + 20/3 = 0`
x2 + 1 = 0
\[4 x^2 + 1 = 0\]
\[x^2 + 2x + 5 = 0\]
\[x^2 - x + 1 = 0\]
\[x^2 + x + 1 = 0\]
\[17 x^2 - 8x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[17 x^2 + 28x + 12 = 0\]
\[21 x^2 - 28x + 10 = 0\]
\[x^2 + x + \frac{1}{\sqrt{2}} = 0\]
\[x^2 - 2x + \frac{3}{2} = 0\]
\[3 x^2 - 4x + \frac{20}{3} = 0\]
Solving the following quadratic equation by factorization method:
\[x^2 - \left( 2\sqrt{3} + 3i \right) x + 6\sqrt{3}i = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2i} = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Write the number of real roots of the equation \[(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0\].
If \[2 + \sqrt{3}\] 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 \[- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}\].
For the equation \[\left| x \right|^2 + \left| x \right| - 6 = 0\] ,the sum of the real roots is
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 value of a such that \[x^2 - 11x + a = 0 \text { and } x^2 - 14x + 2a = 0\] may have a common root is
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 =
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 the difference of the roots of \[x^2 - px + q = 0\] is unity, then
Find the value of P such that the difference of the roots of the equation x2 – Px + 8 = 0 is 2.
Show that `|(z - 2)/(z - 3)|` = 2 represents a circle. Find its centre and radius.
