Please guide me for solving this question. The polynomials chapter is very important. I want the solution of this exercise 2.2 question no.2 solution. How can i easily solve it. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) 1/4 , -1(ii)√2, 1/3(iii) 0, √5(iv) 1, 1(v) -1/4, 1/4vi) 4, 1

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# Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) 1/4 , -1(ii)√2, 1/3(iii) 0, √5(iv) 1, 1(v) -1/4, 1/4vi) 4, 1 Q.2

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(i) 1/4 , -1

Solution:

From the formulas of sum and product of zeroes, we know,

Sum of zeroes = α+β

Product of zeroes = α β

Sum of zeroes = α+β = 1/4

Product of zeroes = α β = -1

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-

x

^{2}–(α+β)x +αβ = 0x

^{2}–(1/4)x +(-1) = 04x

^{2}–x-4 = 0Thus,4x

^{2}–x–4 is the quadratic polynomial.(ii)√2, 1/3

Solution:

Sum of zeroes = α + β =√2

Product of zeroes = α β = 1/3

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-

x

^{2}–(α+β)x +αβ = 0x

^{2}–(√2)x + (1/3) = 03x

^{2}-3√2x+1 = 0Thus, 3x

^{2}-3√2x+1 is the quadratic polynomial.(iii) 0, √5

Solution:

Given,

Sum of zeroes = α+β = 0

Product of zeroes = α β = √5

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly

as:-

x

^{2}–(α+β)x +αβ = 0x

^{2}–(0)x +√5= 0Thus, x

^{2}+√5 is the quadratic polynomial.(iv) 1, 1

Solution:

Given,

Sum of zeroes = α+β = 1

Product of zeroes = α β = 1

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-

x

^{2}–(α+β)x +αβ = 0x

^{2}–x+1 = 0Thus , x

^{2}–x+1is the quadratic polynomial.(v) -1/4, 1/4

Solution:

Given,

Sum of zeroes = α+β = -1/4

Product of zeroes = α β = 1/4

x

^{2}–(α+β)x +αβ = 0x

^{2}–(-1/4)x +(1/4) = 04x

^{2}+x+1 = 0Thus,4x

^{2}+x+1 is the quadratic polynomial.(vi) 4, 1

Solution:

Given,

Sum of zeroes = α+β =

Product of zeroes = αβ = 1

x

^{2}–(α+β)x+αβ = 0x

^{2}–4x+1 = 0Thus, x

^{2}–4x+1 is the quadratic polynomial.