Question

Find the quadratic polynomial if its zeroes are 0, √5.

Answer 1

Answer:

Factorise the equation 4x2 – 4x – 8 = 0

4x2 – 4x – 8 = 0

4x2 – 2x – 2x + 1 = 0

2x(2x – 1) – 1(2x -1) = 0

(2x – 1) (2x – 1) = 0

So, the roots of 4x2 – 4x – 8 are (½ and ½)

Relation between the sum of zeroes and coefficients:

½ + ½ = 1 = -4/-4 i.e. (- coefficient of x/ coefficient of x2)

Relation between the product of zeroes and coefficients:

½ × ½ = ¼ i.e (constant/coefficient of x2)

4. Find the quadratic polynomial if its zeroes are 0, √5.

Solution:

A quadratic polynomial can be written using the sum and product of its zeroes as:

x2 +(α + β)x + αβ = 0

Where α and β are the roots of the polynomial equation.

Here, α = 0 and β = √5

So, the equation will be:

x2 +(0 + √5)x + 0(√5) = 0

Or, x2 + √5x = 0

Answer 2

A quadratic polynomial can be written using the sum and product of its zeroes as: x² + (α+β) + αβ = 0

Where α and β are the roots of the equation.

$\sf \: \: \: \: \: \bullet \alpha = 0 \\ \: \: \:\: \: \sf \bullet \beta = root 5$

$\bf \underline{Equation}:$

☛ x² + ( 0+√5)x + 0 = 0

$\boxed{x {}^{2} + \sqrt{5}x = 0}$

$\\ \bf \therefore {\underline{quadratic \: polinomial \: is \: {x}^{2} + \sqrt{5} x }}$