Advertisements
Advertisements
Question
Find the sum of squares of roots of the equation `2x^4 - 8x^3 + 6x^2 - 3` = 0
Advertisements
Solution
The given equation is 2x4 – 8x3 + 6x2 – 3 = 0.
(÷ 2) ⇒ `x^4 - 4x^3 + 3x^2 - 3/2` = 0
Let the roots be α, β, γ, δ
α + β + γ + δ = – b = 4
(αβ + βγ + γδ + αδ + αγ + βδ) = c = 3
αβγ + βγδ + γδα = – d = 0
αβγδ = `(-3)/2`
To Find α2 + β2 + γ2 + δ2 = (α + β + γ + δ)2 – 2(αβ +
βγ + γδ + αδ + αγ + βδ)
= (4)2 – 2(3)
= 16 – 6
= 10
APPEARS IN
RELATED QUESTIONS
Construct a cubic equation with roots 1, 2 and 3
Construct a cubic equation with roots 1, 1, and – 2
Construct a cubic equation with roots `2, 1/2, and 1`
If α, β and γ are the roots of the cubic equation x3 + 2x2 + 3x + 4 = 0, form a cubic equation whose roots are 2α, 2β, 2γ
If α, β and γ are the roots of the cubic equation x3 + 2x2 + 3x + 4 = 0, form a cubic equation whose roots are `1/alpha, 1/beta, 1/γ`
If α, β and γ are the roots of the cubic equation x3 + 2x2 + 3x + 4 = 0, form a cubic equation whose roots are `- alpha, -beta, -γ`
Solve the equation 3x3 – 16x2 + 23x – 6 = 0 if the product of two roots is 1
Solve the equation x3 – 9x2 + 14x + 24 = 0 if it is given that two of its roots are in the ratio 3 : 2
If α, β, and γ are the roots of the polynomial equation ax3 + bx2 + cx + d = 0, find the value of `sum alpha/(betaγ)` in terms of the coefficients
If α, β, γ and δ are the roots of the polynomial equation 2x4 + 5x3 – 7x2 + 8 = 0, find a quadratic equation with integer coefficients whose roots are α + β + γ + δ and αβγδ
If p and q are the roots of the equation lx2 + nx + n = 0, show that `sqrt("p"/"q") + sqrt("q"/"p") + sqrt("n"/l)` = 0
If the equations x2 + px + q = 0 and x2 + p’x + q’ = 0 have a common root, show that it must be equal to `("pq'" - "p'q")/("q" - "q")` or `("q" - "q'")/("p'" - "P")`
