Advertisements
Advertisements
प्रश्न
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
Advertisements
उत्तर
Given equation z4 - 10z2 + 9 = 0
Putting z2 = x, then given equation reduces to the form x2 - 10x + 9 = 0
⇒ x2 - 9x - x + 9 = 0
⇒ x(x - 9) -1(x - 9) = 0
⇒ (x - 9) (x - 1) = 0
⇒ x - 9 = 0 or x - 1 = 1
⇒ x = 9 or x = 1
But z2 = x
∴ z2 = 9
⇒ z = ±3
or
z2 = 1
z = ±1
Hence, the required roots are ±3, ±1.
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
Find the value of k for which the roots of the equation 3x2 - 10x + k = 0 are reciprocal of each other.
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
