Advertisements
Advertisements
प्रश्न
Solve the cubic equation: 2x3 – x2 – 18x + 9 = 0 if sum of two of its roots vanishes
उत्तर
The given equation is 2x3 – x2 – 18x + 9 = 0
`x^3 - x^2/2 - 9x + 9/2` = 0
Let the roots be α, – α, β
`alpha - alpha + beta = - ((-1)/2)`
⇒ `beta = 1/2`
`(alpha)(- alpha) (beta) = (- 9)/2`
⇒ `= alpha^2 (1/2) = (- 9)/2`
α2 = 9
α = ± 3
The roots are 3, `- 3, 1/2`
APPEARS IN
संबंधित प्रश्न
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:
8x3 – 2x2 – 7x + 3 = 0
Solve the equation:
x4 – 14x2 + 45 = 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:
A zero of x3 + 64 is
Choose the correct alternative:
The polynomial x3 – kx2 + 9x has three real roots if and only if, k satisfies
Choose the correct alternative:
If x3 + 12x2 + 10ax + 1999 definitely has a positive zero, if and only if
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
