MyQuestionIcon

1

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

Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the root of a quadratic equation $x^{2} - 3 x + 5 = 0$ , then the equation whose roots are $(α^{2} - 3 α + 7) and (β^{2} - 3 β + 7)$ is

A

x^{2} + 4 x + 4 = 0

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

B

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

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

C

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

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

D

x^{2} + 2 x + 3 = 0

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

Open in App

Solution

The correct option is B $x^{2} - 4 x + 4 = 0$
Given $α, β$ are the roots of equation $x^{2} - 3 x + 5 = 0$
So,
$α^{2} - 3 α + 5 = 0 β^{2} - 3 β + 5 = 0$
$∴ α^{2} - 3 α = - 5 and β^{2} - 3 β = - 5$
Now,
$α^{2} - 3 α + 7 = 2 and β^{2} - 3 β + 7 = 2$

Hence, the quadratic equation whose roots are $2, 2$ is
$(x - 2)^{2} = 0 ∴ x^{2} - 4 x + 4 = 0$

Suggest Corrections

thumbs-up

13

Similar questions

α, β

are the root of a quadratic equation

x^{2} - 3 x + 5 = 0

, then the equation whose roots are

(α^{2} - 3 α + 7)

(β^{2} - 3 β + 7)

α, β

are the roots of the equation

x^{2} + 4 x - 1 = 0

, then the equation whose roots are

3 α - 5, 3 β - 5

α, β

are the roots of the equation

x^{2} - a x + b = 0

and roots of the eqaution

b x^{2} - 4 x + 4 = 0

α + \frac{β^{2}}{α}

β + \frac{α^{2}}{β}

a + b

^{'} α^{'}

^{'} β^{'}

are the roots of quadratic equation

x^{2} + 4 x + 1 = 0

, then find the value of

\frac{1}{α^{2}} + \frac{1}{β^{2}}

α

β^{2}

are the roots of the equation

8 x^{2} - 10 x + 3 = 0,

β^{2} > \frac{1}{2},

then an equation whose roots are

(α + i β)^{100}

(α - i β)^{100}

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Relation between Roots and Coefficients for Quadratic

Standard XIII Mathematics

Join BYJU'S Learning Program

CrossIcon