Login/Sign Up
Find the zeroes of the quadratic polynomial $f(x)=5 x^{2}-4-8 x$ and verify the relationship between the zeroes and coefficients of the given polynomial.
Find the zeroes of the quadratic polynomial $f(x)=5 x^{2}-4-8 x$ and verify the relationship between the zeroes and coefficients of the given polynomial.
CBSE | Class 10 | Excercise 2A | Polynomials
Find the zeroes of the quadratic polynomial $f(x)=5 x^{2}-4-8 x$ and verify the relationship between the zeroes and coefficients of the given polynomial.

$f(x)=5 x^{2}-4-8 x$

$=5 x^{2}-8 x-4$

$=5 x^{2}-(10 x-2 x)-4$

$=5 x^{2}-10 x+2 x-4$

$=5 x(x-2)+2(x-2)$

$=(5 x+2)(x-2)$

$\therefore \mathrm{f}(\mathrm{x})=0 \Rightarrow(5 \mathrm{x}+2)(\mathrm{x}-2)=0$

$\Rightarrow 5 x+2=0$ or $x-2=0$

$\Rightarrow \mathrm{x}=\frac{-2}{5}$ or $\mathrm{x}=2$

So, the zeroes of $\mathrm{f}(\mathrm{x})$ are $\frac{-2}{5}$ and 2 .

Sum of zeroes $=\left(\frac{-2}{5}\right)+2=\frac{-2+10}{5}=\frac{8}{5}=\frac{-(\text { coefficient of } x)}{\left(\text { coefficient of } x^{2}\right)}$

Product of zeroes $=\left(\frac{-2}{5}\right) \times 2=\frac{-4}{5}=\frac{\text { constant term }}{\left(\text { coefficient of } x^{2}\right)}$

i

More Material