Let - be the zeros of a polynomial px- If -24 -8- then find quadratic polynomial-

Α + β = 24 α β = 8 Adding both the equations we get 2×α = 32 α = 16 Subtracting both the equations we get 2×β = 16 β = 8 α + β = 24 α×β = 128 p(x)= x^2 (su ...

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

Byju's Answer

Standard X

Mathematics

Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

Let α&β be th...

Question

Let $α & β$ be the zeros of a polynomial p(x). If $α + β = 24 & α - β = 8$ , then find quadratic polynomial.

Open in App

Solution

$α + β = 24$
$α - β = 8$
Adding both the equations we get
$2 \times α = 32$
$α = 16$
Subtracting both the equations we get
$2 \times β = 16$
$β = 8$
$α + β = 24$
$α \times β = 128$
p(x)= $x^{2}$ - (sum of zeroes)x + Product of zeroes
$x^{2}$ - 24x + 128

Suggest Corrections

Similar questions

Q. If

α

and

β

are the zeros of the quadratic polynomial such that

α + β = 24

and

α - β = 8

find a quadratic polynomial having a

α

and

β

as its zeros.

Q. If

α

and

β

are zeros of a quadratic polynomial such that

α + β = 24

and

α - β = 8

find a quadtratic polynomial having

α

and

β

as it's zeros.

Q. If

α

and

β

are the zeros of polynomial

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

and

α + β = α . β

then

k

Q. If

α, β

are zeroes of the polynomial

p (x) = x^{2} - x - 4

, then find the value of

\frac{α}{β} + \frac{β}{α} + 3 (\frac{1}{α} + \frac{1}{β}) - 2 α β

Join BYJU'S Learning Program

Let α&β be the zeros of a polynomial p(x). If α+β=24 & α−β=8, then find quadratic polynomial.

α+β=24 α−β=8 Adding both the equations we get 2×α=32 α=16 Subtracting both the equations we get 2×β=16 β=8 α+β=24 α×β=128 p(x)= x2 - (sum of zeroes)x + Product of zeroes x2 - 24x + 128

Let $α & β$ be the zeros of a polynomial p(x). If $α + β = 24 & α - β = 8$ , then find quadratic polynomial.

$α + β = 24$
$α - β = 8$
Adding both the equations we get
$2 \times α = 32$
$α = 16$
Subtracting both the equations we get
$2 \times β = 16$
$β = 8$
$α + β = 24$
$α \times β = 128$
p(x)= $x^{2}$ - (sum of zeroes)x + Product of zeroes
$x^{2}$ - 24x + 128