Question

If the zeros of a polynomial are -√2 and √2, then the equation of the polynomial is-​

Answer 1

Answer:

The Given Zeroes: -√2 and √2.

We know that a quadratic equation is in the form ax²+bx+c = 0

And we know the relation between the coefficients and x.

If we take α as one zero(√2) and β as the other(-√2), then,

α+β = $\frac{-b}{a}$

and,

αβ = $\frac{c}{a}$.

[[Now, to solve this, a is usually considered as 1. And if while considering a as 1, the value of b and c are fractions, then the whole equation is multiplied by the required number.]]

α+β = $\frac{-b}{a}$

-√2 +  √2 = $\frac{-b}{a} = \frac{-b}{1} = -b$

0 = -b

b = 0

So, x has no co-efficient, since b is 0.

αβ = $\frac{c}{a}$

-√2 × √2 = $\frac{c}{a}$ $= \frac{c}{1} = c$

-2 = c

c = -2

So, the constant term is -2.

After all of this, we end up with this summary:

The Co-efficient of x² is 1(a)

The Co-efficient of x is 0(b)

The Constant is -2(c)

So, the equation would be:

x²-2

Hope it Helps,

Byeeee