MyQuestionIcon

1

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

Transformation of Roots: Linear Combination of Roots

If α, β are t...

Question

If $α, β$ are the roots of $x^{2} + 7 x + 5 = 0$ , then the equation whose roots are $α - 1, β - 1$ is

A

x^{2} + 7 x + 13 = 0

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

B

x^{2} + 5 x + 1 = 0

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

C

x^{2} + 9 x + 13 = 0

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

D

x^{2} + 5 x - 1 = 0

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

Open in App

Solution

The correct option is C $x^{2} + 9 x + 13 = 0$
$f (x) = x^{2} + 7 x + 5 = 0 \to roots are α, β$
The equation whose roots are $α - 1, β - 1$ is,
$f (x + 1) = 0$
$\Rightarrow (x + 1)^{2} + 7 (x + 1) + 5 = 0 \Rightarrow x^{2} + 2 x + 1 + 7 x + 7 + 5 = 0 \Rightarrow x^{2} + 9 x + 13 = 0$

Suggest Corrections

thumbs-up

0

Similar questions

α, β

are the roots of

x^{2} + 7 x + 5 = 0

, then the equation whose roots are

α - 1, β - 1

α, β

are the roots of

x^{2} + 7 x + 5 = 0

, then the equation whose roots are

α - 1, β - 1

α, β

are roots of the quadratic equation

x^{2} - x - 1 = 0,

then the quadratic equation whose roots are

\frac{1 + α}{2 - α}, \frac{1 + β}{2 - β}

α, β, γ

are roots of equation

x^{3} - x - 1 = 0

, then the equation whose roots are

\frac{1}{β + γ}, \frac{1}{γ + α}, \frac{1}{α + β}

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Transformation of Roots: Linear Combination of Roots

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Transformation of Roots: Linear Combination of Roots

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon