Advertisements
Advertisements
प्रश्न
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
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.
APPEARS IN
संबंधित प्रश्न
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Form the quadratic equation if its roots are –3 and 4.
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
