Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let α, β be the roots of the equation.
Therefore, α + β = a – 2 and αβ = –( a + 1)
Now α2 + β2 = (α + β)2 – 2αβ
= (a – 2)2 + 2(a + 1)
= (a – 1)2 + 5
Therefore, α2 + β2 will be minimum if (a – 1)2 = 0, i.e., a = 1.
APPEARS IN
संबंधित प्रश्न
Solve the equation x2 + 3x + 9 = 0
Solve the equation `x^2 + x + 1/sqrt2 = 0`
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2 – Imz1 Imz2
Solve the equation 21x2 – 28x + 10 = 0
x2 + 1 = 0
9x2 + 4 = 0
\[4 x^2 + 1 = 0\]
\[x^2 + 2x + 5 = 0\]
\[x^2 + x + 1 = 0\]
\[27 x^2 - 10 + 1 = 0\]
\[8 x^2 - 9x + 3 = 0\]
\[2 x^2 + x + 1 = 0\]
\[\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0\]
\[\sqrt{5} x^2 + x + \sqrt{5} = 0\]
Solve the following quadratic equation:
\[i x^2 - 4 x - 4i = 0\]
Solve the following quadratic equation:
\[2 x^2 + \sqrt{15}ix - i = 0\]
Solve the following quadratic equation:
\[2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0\]
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 \[(a - b) x^2 + (b - c)x + (c - a) = 0\] .
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
The values of k for which the quadratic equation \[k x^2 + 1 = kx + 3x - 11 x^2\] has real and equal roots are
The set of all values of m for which both the roots of the equation \[x^2 - (m + 1)x + m + 4 = 0\] are real and negative, is
If the difference of the roots of \[x^2 - px + q = 0\] is unity, then
The least value of k which makes the roots of the equation \[x^2 + 5x + k = 0\] imaginary is
Show that `|(z - 2)/(z - 3)|` = 2 represents a circle. Find its centre and radius.
If `|(z - 2)/(z + 2)| = pi/6`, then the locus of z is ______.
