Question

if the zeeoes of quadratic equation are 1/2 & -1/2 find the quadratic equation.​

Answer 1

Zeroes are 1/2 and -1/2.

Thus, putting either of the zeroes in the quadratic should give us zero as the answer.

Consider:

$(x+\frac{1}{2})(x-\frac{1}{2})=0$

This satisfies x=1/2 and x=-1/2. Hence it is the required quadratic equation.

$\implies x^2-\frac{1}{4}=0\\</p><p>\implies x^2=\frac{1}{4}\\</p><p>\color{red}{4x^2-1=0}$

Answer 2

Step-by-step explanation:

Here ,

a = 1/2

&

b = -(1/2)

The req. polynomial is,

x^2 - (a+b)x + (ab)

x^2 - (1/2-1/2)x + (1/2×-1/2)

x^2 - 0x - 1/4

x^2 - 1/4

1/4(x^2 - 1)