Express r in terms of p and q- if the roots of the equation x2 - px - q - 0 are - and the roots of the equationx2 - rx - s - 0 are -4-4

Α + β nbsp;= p, αβ = q α^4 + β^4 nbsp; = r nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; =(α^2 + β^2)^2 2α^2β^2 nbsp; nbsp; nb ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Mathematics

Algebra of Roots of Quadratic Equations

Express r in ...

Question

Express $r$ in terms of $p$ and $q$ , if the roots of the equation $x^{2} + p x + q = 0$ are $α, β$ and the roots of the equation
$x^{2} - r x + s = 0$ are $α^{4}, β^{4}$

$2 q^{2}$ - $(p^{2} - 2 q)^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$p - 2 q^{2} - 2 q$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$2 q - p - 2 q^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(p^{2} - 2 q)^{2}$ - $2 q^{2}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$(p^{2} - 2 q)^{2}$ - $2 q^{2}$

$α + β = - p, α β = q$
$α^{4} + β^{4} = r$
$= (α^{2} + β^{2})^{2}$ - 2 $α^{2} β^{2}$
$= ((α + β)^{2} - 2 α β)^{2} - 2 α^{2} β^{2}$
$r = (p^{2} - 2 q)^{2} - 2 q^{2}$

Suggest Corrections

Similar questions

Express $r$ in terms of $p$ and $q$ , if the roots of the equation $x^{2} + p x + q = 0$ are $α, β$ and the roots of the equation
$x^{2} - r x + s = 0$ are $α^{4}, β^{4}$

Q. Suppose

p, q, r, s \in R

and

α, β

be the roots of

x^{2} + p x + q = 0

and

α^{4}, β^{4}

be the roots of

x^{2} - r x + s = 0

. If

| α | \neq | β |

then the equation

x^{2} - 4 q x + 2 q^{2} - r = 0

has always

Q. lf

α

and

β

are the roots of

x^{2} + p x + q = 0

and

α^{4}, β^{4}

are the roots of

x^{2} - r x + s = 0

, then the equation

x^{2} - 4 q x + (2 q^{2} - r) = 0

has

Express r in terms of p and q if the roots of the equation $x^{2} + p x + q = 0$ are $α, β$ and the roots of the equation
$x^{2} - r x + s = 0$ are $α^{4}, β^{4}$

Q. If

α

and

β

are the roots of

x^{2} + p x + q = 0

and

α^{4}, β^{4}

are the roots of

x^{2} - r x + s = 0,

then the equation

x^{2} - 4 q x + 2 q^{2} - r = 0,

has always two real roots.

Join BYJU'S Learning Program

Express r in terms of p and q, if the roots of the equation x2+px+q=0 are α,β and the roots of the equation x2−rx+s=0 are α4,β4

The correct option is D (p2−2q)2 - 2q2 α+β=−p, αβ=q α4+β4=r =(α2+β2)2 - 2α2β2 =((α+β)2−2αβ)2−2α2β2 r=(p2−2q)2−2q2

Express $r$ in terms of $p$ and $q$ , if the roots of the equation $x^{2} + p x + q = 0$ are $α, β$ and the roots of the equation
$x^{2} - r x + s = 0$ are $α^{4}, β^{4}$

The correct option is D
$(p^{2} - 2 q)^{2}$ - $2 q^{2}$

$α + β = - p, α β = q$
$α^{4} + β^{4} = r$
$= (α^{2} + β^{2})^{2}$ - 2 $α^{2} β^{2}$
$= ((α + β)^{2} - 2 α β)^{2} - 2 α^{2} β^{2}$
$r = (p^{2} - 2 q)^{2} - 2 q^{2}$