CameraIcon

SearchIcon

MyQuestionIcon

1

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

Quadratic Formula

If αand β...

Question

If $α$ and $β$ are the zeros of the quadratic polynomial $f (t) = t^{2} - 4 t + 3$ , find the value of $α^{4} β^{3} + α^{3} β^{4} .$

Open in App

Solution

$f (t) = t^{2} - 4 t + 3$
$α + β = 4$
$α β = 3$
$α^{4} β^{3} + α^{3} β^{4}$
$= α^{3} β^{3} (α + β)$
$= (3)^{3} \times 4$
$= 108$

Suggest Corrections

thumbs-up

0

Similar questions

α, β

are the zeroes of the polynomial

x^{2} - 2 x + 2

find the value of
i)

α^{2} + β^{2}

\frac{α}{β} + \frac{β}{α}

α^{3} + β^{3}

\frac{α^{2}}{β} + \frac{β^{2}}{α}

α^{4} + β^{4}

α, β

are the roots of the quadratic equation

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

, then the values of

α^{3} + β^{3}

α^{4} + α^{2} β^{2} + β^{4}

are respectively

α, β

are zeroes of the polynomial

p (x) = {2 x}^{2} - 7 x + 3,

find the value of

α^{3} β^{3}

α

β

be two zeros of the quadratic polynomial

a x^{2} + b x + c

, then evaluate:

α^{3} + β^{3}

α + β + γ = 6, α^{2} + β^{2} + γ^{2} = 14

α^{3} + β^{3} + γ^{3} = 36

α^{4} + β^{4} + γ^{4} =

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Solving QE using Quadratic Formula

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Quadratic Formula

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon