Home
Class 12
MATHS
If alpha,beta are the roots of x^(2)-3 ...

If `alpha,beta` are the roots of `x^(2)-3 x+5=0` and `gamma, delta` are the roots of `x^(2)+5 x-3=0`, then the equation whose roots are `alpha gamma+beta delta` and `alpha delta+beta gamma` is

A

`x^(2)-15x-158=0`

B

`x^(2)+15x-158=0`

C

`x^(2)-15x+158=0`

D

`x^(2)+15x+158=0`

Text Solution

Verified by Experts

`:'alpha+beta=3, alpha beta=5, gamma +delta=(-5),gamma delta=(-3)`
Sum of roots `=(alpha gamma +beta delta)=(alpha delta +beta gamma)`
`=(alpha +beta)(gamma+delta)=3xx(-5)=(-15)`
Product of roots `=(alpha gamma+beta delta)(alpha delta +beta gamma)`
`=alpha^(2) gama delta +alpha beta gamma^(2)+beta alpha delta^(2)+beta^(2) gamma delta`
`=gamma delta(alpha^(2)+beta^(2))+alpha beta (gamma^(2)+delta^(2))`
`=-3(alpha^(2)+beta^(2))+5(gamma^(2)+delta^(2))`
`=-3[(alpha+beta)^(2)-2alpha beta]+5[(gamma+delta)^(2)-2gamma delta]`
`=-3[9-10]+5[25+6]=158`
`:.` Required equation is `x^(2)+15x+158=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha , beta are the roots of 2 x^(2)-x+7=0 then the equation whose roots are 2-3 alpha and 2-3 beta is

If alpha and beta are the rotos of a x^(2)+b x+c=0 the equation whose roots are 2+alpha and 2+beta is

If alpha, beta are the roots of x^(2)-3x+1=0 , then the equation whose roots are (1/(alpha-2),1/(beta-2)) is

Let alpha, beta be the roots of x^(2)+x+1=0 . The equation whose roots are alpha^(25) and beta^(22) .

If alpha and beta are the roots of x^(2) + qx + 1 = 0 and gamma, delta the roots of x^(2) + qx + 1 = 0 , then the value of (alpha - gamma ) (beta - gamma ) (a + delta ) beta + delta) is :

If alpha, beta are the roots of the equation x^(2)+x+1=0 , then the equation whose roots are (alpha)/(beta) and (beta)/(alpha) is

If alpha, beta are the roots of a x^(2)+b x+c=0 the equation whose roots are alpha+(1)/(beta) and beta+(1)/(alpha) is

If alpha and beta are the roots of the equation 2x^2-3x + 4=0 , then the equation whose roots are alpha^2 and beta^2, is

If alpha, beta are the roots of a x^(2)+b x+c=0 the equation whose roots are (alpha+beta)^(-1) , alpha^(-1)+ beta^(-1) is

Let alpha, beta be the roots of x^(2)+a x+1=0 . Then the equation whose roots are – (alpha+(1)/(beta)) and -(beta+(1)/(alpha))