Advertisements
Advertisements
प्रश्न
The least value of k which makes the roots of the equation \[x^2 + 5x + k = 0\] imaginary is
पर्याय
4
5
6
7
उत्तर
7
The roots of the quadratic equation \[x^2 + 5x + k = 0\] will be imaginary if its discriminant is less than zero.
\[\therefore 25 - 4k < 0\]
\[ \Rightarrow k > \frac{25}{4}\]
Thus, the minimum integral value of k for which the roots are imaginary is 7.
APPEARS IN
संबंधित प्रश्न
Solve the equation 27x2 – 10x + 1 = 0
Solve the equation 21x2 – 28x + 10 = 0
x2 + 1 = 0
x2 + 2x + 5 = 0
x2 + x + 1 = 0
\[x^2 + 2x + 5 = 0\]
\[21 x^2 + 9x + 1 = 0\]
\[x^2 - x + 1 = 0\]
\[17 x^2 - 8x + 1 = 0\]
\[17 x^2 + 28x + 12 = 0\]
\[21 x^2 - 28x + 10 = 0\]
\[- x^2 + x - 2 = 0\]
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:
\[x^2 - \left( 2\sqrt{3} + 3i \right) x + 6\sqrt{3}i = 0\]
Solve the following quadratic equation:
\[x^2 - \left( 5 - i \right) x + \left( 18 + i \right) = 0\]
Solve the following quadratic equation:
\[\left( 2 + i \right) x^2 - \left( 5 - i \right) x + 2 \left( 1 - i \right) = 0\]
Solve the following quadratic equation:
\[x^2 - x + \left( 1 + i \right) = 0\]
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
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 \[(a - b) x^2 + (b - c)x + (c - a) = 0\] .
If a and b are roots of the equation \[x^2 - x + 1 = 0\], then write the value of a2 + b2.
Write the number of quadratic equations, with real roots, which do not change by squaring their roots.
If α, β are roots of the equation \[x^2 - a(x + 1) - c = 0\] then write the value of (1 + α) (1 + β).
If a, b are the roots of the equation \[x^2 + x + 1 = 0, \text { then } a^2 + b^2 =\]
If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to
The values of x satisfying log3 \[( x^2 + 4x + 12) = 2\] are
If α, β are the roots of the equation \[x^2 + px + 1 = 0; \gamma, \delta\] the roots of the equation \[x^2 + qx + 1 = 0, \text { then } (\alpha - \gamma)(\alpha + \delta)(\beta - \gamma)(\beta + \delta) =\]
If x is real and \[k = \frac{x^2 - x + 1}{x^2 + x + 1}\], then
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 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, β are the roots of the equation \[x^2 - p(x + 1) - c = 0, \text { then } (\alpha + 1)(\beta + 1) =\]
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.
