Question

Verify the relationship between the zeros and the cofficients of the polynomial $p\left(x\right)=2x^2-7x+3$.

Answer 1

$p\left(x\right)=2x^2-7x+3$

$\Rightarrow p\left(x\right)=2x^2-6x-x+3$

$\Rightarrow p\left(x\right)=(2x-1)(x-3)$

Let the roots be $\alpha ,\beta =\frac{1}{2},3$

We know $\alpha \cdot \beta =\frac{c}{a}$

$\Rightarrow 3\cdot \frac{1}{2}=\frac{3}{2}$

$\alpha +\beta =\frac{1}{2}+3=\frac{7}{2}=\frac{-b}{a}$