Question

Find the quadratic polynomial, for the zeroes a, ß given in each case.
2,-1
✓3,-✓3
1/4,-1
1/2,3/2​

Answer 1

Answer:

i) 2,-1

α+β= sum of zeroes = 2

α β = product of zeroes = -1

Quadratic polynomial is in form of:

x2 + (a+b)x + a*b

=> X2 + 2 x + -1 is the polynomial expression of zeroes 2,-1.

ii)√3,-√3

α+β = sum of zeroes = √3

α β = product of zeroes = -√3

Quadratic polynomial is in form of:

x2 - (a+b)x + a*b

=> X2 -√3x -√3

is the polynomial expression of zeroes -√3,√3.

iii) 1/4,-1

α+β= sum of zeroes = 1/4

α β = product of zeroes = -1

Quadratic polynomial is in form of:

x2 - (α+β)x + αβ

x2–(α+β)x +αβ = 0

x2–(1/4)x +(-1) = 0

4x2–x-4 = 0

Thus,4x2–x–4 is the quadratic polynomial.

iv)1/2,3/2

Sum of zeroes = α+β =1/2

Product of zeroes = αβ = 3/2

Quadratic polynomial is in form of:

x2 + (α+β)x + αβ

x2–(α+β)x +αβ = 0

x2–(1/2)x +(3/2) = 0

2x2 - x + 3 = 0

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