Advertisements
Advertisements
Question
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
Advertisements
Solution
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.
RELATED QUESTIONS
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
Solve the following quadratic equation using formula method only :
x2 +10x- 8= 0
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
The roots of the equation 7x2 + x – 1 = 0 are:
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Every quadratic equations has at most two roots.
