Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively.

(i) 1/4, -1

(ii) 1,1

(iii) 4, 1​

Answer 1

Step-by-step explanation:

Solution:

(i) From the formulas of sum and product of zeroes, we know,

Sum of zeroes = α + β

Product of zeroes = αβ

Given,

Sum of zeroes = 1/4

Product of zeroes = -1

Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:-

x2 – (α + β)x + αβ

x2 – (1/4)x + (-1)

4x2 – x – 4

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

(ii) Given,

Sum of zeroes = 1 = α + β

Product of zeroes = 1 = αβ

Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:-

x2 – (α + β)x + αβ

x2 – x + 1

Thus, x2 – x + 1 is the quadratic polynomial.

(iii) Given,

Sum of zeroes, α + β = 4

Product of zeroes, αβ = 1

Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:-

x2 – (α + β)x + αβ

x2 – 4x + 1

Thus, x2 – 4x +1 is the quadratic polynomial.

Answer 2

Step-by-step explanation:

(i) On substituting the value of formula we get

x² –(1/4)x -1 = 0

Multiply by 4 to remove denominator we get

4x² – x -4 = 0

(ii) On substituting the value of formula we get

x² –(1)x + 1 = 0

simplify it we get

x² – x + 1 = 0

(iii)

On substituting the value of formula we get

x² –(4)x + 1 = 0

x^2 –4x + 1 = 0