Let - - be the roots of the equation x2-px-r-0 and -2-2- be the roots of the equation x2-qx-r-0- Then the value of r is

The correct option is D 2/9 ( 2p q ) ( 2q p ) α +β =p, nbsp;α2+2β =q, nbsp;αβ =r Solve the above equation and get α =4p 2q3, nbsp; β=2q ...

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

Byju's Answer

Standard XII

Mathematics

Higher Order Equations

Let α ,β be...

Question

Let $α, β$ be the roots of the equation $x^{2} - p x + r = 0$ and $α / 2, 2 β$ be the roots of the equation $x^{2} - q x + r = 0.$ Then the value of $r$ is

2 / 9 (p - q) (2 q - p)

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

2 / 9 (q - p) (2 p - q)

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

2 / 9 (q - 2 p) (2 q - p)

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

2 / 9 (2 p - q) (2 q - p)

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

Open in App

Solution

The correct option is D $2 / 9 (2 p - q) (2 q - p)$
$α + β = p, \frac{α}{2} + 2 β = q, α β = r$
Solve the above equation and get
$α = \frac{4 p - 2 q}{3}, β = \frac{2 q - p}{3}$
So, $r = α β = \frac{2}{9} (2 q - p) (2 p - q)$
Hence, option 'D' is correct.

Suggest Corrections

Similar questions

Q. Let

α, β

be the roots of the equation

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

and

\frac{α}{2}, 2 β

be the roots of the equation

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

then the value of r is

Let $α, β$ be the roots of the equation $x^{2} - p x + r = 0$ and $\frac{α}{2}, 2 β$ be the roots of the equation $x^{2} - q x + r = 0$ . Then, the value of $r$ is:

Q. If a and b are the roots of the equation x² – px + r = 0 and a/2 and 2b be the roots of the equation x² – qx + r = 0. Then the value of r is:

Q. If a and b are the roots of the equation

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

and

\frac{a}{2}

and 2b be the roots of the equation

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

. Then the value of r is:

Q. Let

α, β \in R

. If

α, β^{2}

are the roots of quadratic equation

x^{2} - p x + 1 = 0

and

α^{2}, β

equation

x^{2} - q x + 8 = 0

, then the value r if

\frac{r}{8}

is the arithmetic means of p and q, is

Join BYJU'S Learning Program

Let α,β be the roots of the equation x2−px+r=0 and α/2,2β be the roots of the equation x2−qx+r=0. Then the value of r is

The correct option is D 2/9(2p−q)(2q−p)α+β=p,α2+2β=q,αβ=rSolve the above equation and getα=4p−2q3,β=2q−p3 So, r=αβ=29(2q−p)(2p−q)Hence, option 'D' is correct.

Let $α, β$ be the roots of the equation $x^{2} - p x + r = 0$ and $α / 2, 2 β$ be the roots of the equation $x^{2} - q x + r = 0.$ Then the value of $r$ is

The correct option is D $2 / 9 (2 p - q) (2 q - p)$
$α + β = p, \frac{α}{2} + 2 β = q, α β = r$
Solve the above equation and get
$α = \frac{4 p - 2 q}{3}, β = \frac{2 q - p}{3}$
So, $r = α β = \frac{2}{9} (2 q - p) (2 p - q)$
Hence, option 'D' is correct.