Question

HEYA MATE....

UR Question: 16
If α and β are the zeroes of the quadratic polynomial such that α + β = 24 and α – β = 8, find a quadratic polynomial having α and β as its zeroes.

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Answer 1

hi there mate!!!

Solution:

Here,

a+B=24 and a-B=8

now

adding both equations,

a+B=24....... (1)

+ a-B =8.......... (2)

2a = 32

a= 32/2=16

substituting value of a in (1)

a+B=24

16+B=24

B=24-16

B=8

hence,

a=16 and B = 8

now,

we know,

the formula for finding a quadratic polynomial:

x^2-(a+B)x+aB=0

x^2-(16+8)x+16×8=0

x^2-24x+128=0.......(required quadratic polynomial)

note: here a= alpha and B= beta

hope this helps!☺❤✌

Answer 2

Heya!

Here is ur answer...

Given, α and β are the zeros of the quadratic polynomial.

Such that,

α+β = 24 --------(1)

α-β = 8 -------(2)

Now, (1) + (2)

α + β = 24

α - β = 8

_______________

2α = 32

α = 32/2

α = 16

By sub. α = 16 in eq.(1),

16+β = 24

β = 24-16

β = 8

And,

α+β = 24

αβ = 16×8 = 128

Now, According to quadratic Formula

k[x² -(α+β)x +αβ]

=> k[x²-(24)x + 128]

=> k[x²-24x +128]

let, k = 1

=> 1[x²-24x +128]

Therefore, the quadratic formula is..

X² -24X +128

Hope it helps u..