Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients :

$x^2+3x-10$

Answer 1

We have $p\left(x\right)=x^2+3x-10=0(x+5)(x-2)=0$

$(x+5)=0or(x-2)=0$

$x=-5orx=2$

Zeroes of $p\left(x\right)=x^2+3x-10$ are $\alpha =-5and\beta =2$

Now, the sum of zeroes $=\alpha +\beta =-5+2=-3$

Sum of zeros $\frac{-b}{a}=\frac{-\left(3\right)}{1}=-3$

Product of zeros $=\alpha \times \beta =-5\times 2=-10$

Product of zeros $\frac{c}{a}=\frac{-10}{1}=-10$

Hence proved that,

um of zeros $=\frac{-\left(Coefficientofx\right)}{Coefficientof{x}^2}$

Product of zeros $=\frac{Constantterm}{Coefficientof{x}^2}$