Question

Find zeroes of polynomial $4x^2-7$ and verify relationship between the zeroes and its coefficients.

Answer 1

Let f(x) = $4x^2+7$

$4x^2-7=0$

${\left(2x\right)}^2-{\left(\sqrt{7}\right)}^2=0$

Using $a^2-b^2$ = (a - b)(a + b), we have

(2x - √7)(2x + √7) = 0

2x - √7 = 0 or 2x + √7 = 0

2x = √7 or 2x = -√7

x = $\frac{\sqrt{7}}{2}$ or x = $-\frac{\sqrt{7}}{2}$ -

α + β = $\frac{\sqrt{7}}{2}+\frac{-\sqrt{7}}{2}=0$ =$\frac{0}{4}=\frac{-b}{a}$

αβ $\frac{\sqrt{7}}{2}\times \frac{-\sqrt{7}}{2}=\frac{-7}{4}=\frac{c}{a}$

So, α + β = $\frac{-b}{a}$ -b/a and αβ = $\frac{c}{a}$