If one of the zero of polynomial is three more than other and sum of the zeroes is 5 then the polynomial is ____

x^{2} + 5 x + 4

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

x^{2} - 5 x + 4

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

x^{2} - 5 x - 4

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

2 x^{2} - 5 x + 4

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

Open in App

Solution

The correct option is B $x^{2} - 5 x + 4$
Given, Let zeroes be $α & β$

Sum of the zeroes, $α + β = 5$
One of the zero is 3 more than other
$\Rightarrow α = β + 3$
$∴ β + 3 + β = 5 2 β = 5 - 3 \Rightarrow β = 1 α = 3 + 1 = 4$

Polynomial is given by, $k [x^{2} - (α + β) x + α β] k [x^{2} - 5 x + 4 \times 1] k [x^{2} - 5 x + 4] x^{2} - 5 x + 4 [k = 1]$

The polynomial is $x^{2} - 5 x + 4$

Suggest Corrections

Similar questions

6 x^{2} + 13 x + k

form a quadratic polynomial one of whose zeroes is 2+ root 5 and the sum of the zeroes is 4

2 + \sqrt{5}

If one zero of the polynomialx²+ kx + 18 is double the other zero then k =?

x^{2} + a

Join BYJU'S Learning Program