Advertisements
Advertisements
Question
Solve the equation:
x4 – 14x2 + 45 = 0
Solution
Put t = x2
⇒ (x2)2 – 14x2 + 45 = 0
t2 – 14t + 45 = 0
t2 – 9t – 5t + 45 = 0
t(t – 9) – 5(t – 9) = 0
(t – 9)(t – 5) = 0
t – 9 = 0 or t – 5 = 0
t = 9 or t = 5
x2 = 9 or x2 = 5
x = ± 3 or y = `+- sqrt(5)`
The roots are ± 3, `+- sqrt(5)`
APPEARS IN
RELATED QUESTIONS
Solve the cubic equation: 2x3 – x2 – 18x + 9 = 0 if sum of two of its roots vanishes
Solve the equation 9x3 – 36x2 + 44x – 16 = 0 if the roots form an arithmetic progression
Solve the equation 3x3 – 26x2 + 52x – 24 = 0 if its roots form a geometric progression
Determine k and solve the equation 2x3 – 6x2 + 3x + k = 0 if one of its roots is twice the sum of the other two roots
Find all zeros of the polynomial x6 – 3x5 – 5x4 + 22x3 – 39x2 – 39x + 135, if it is known that 1 + 2i and `sqrt(3)` are two of its zeros
Solve the cubic equations:
2x3 – 9x2 + 10x = 3
Solve the cubic equations:
8x3 – 2x2 – 7x + 3 = 0
Solve: (x – 5)(x – 7) (x + 6)(x + 4) = 504
Solve: (x – 4)(x – 2)(x- 7)(x + 1) = 16
Solve: (2x – 1)(x + 3)(x – 2)(2x + 3) + 20 = 0
Choose the correct alternative:
If α, β and γ are the zeros of x3 + px2 + qx + r, then `sum 1/alpha` is
Choose the correct alternative:
The polynomial x3 – kx2 + 9x has three real roots if and only if, k satisfies
Choose the correct alternative:
The polynomial x3 + 2x + 3 has
Choose the correct alternative:
The number of positive roots of the polynomials `sum_("j" = 0)^"n" ""^"n""C"_"r" (- 1)^"r" x^"r"` is
