find the quadratic polynomial whose zeros are 1 and -3 verify the rela

1.	find the quadratic polynomial whose zeros are 1 and -3 verify the relation between the coefficient and zeros
Answer» GIVEN : The zeroes of the quadratic equation are 1 and -3 TO VERIFY: The relation between the coefficient and zeroes SOLUTION : Given that the zeroes of the quadratic equation are 1 and -3 Let $\alpha=1$ and $\beta=-3$ be the zeroes of the given quadratic equation. The quadratic equation can be written with the given zeroes is given by: $x^2-(sum of the zeroes)x+product of the zeroes=0$ $sum of the zeroes=\alpha+\beta=1-3$ $=-2$ $sum of the zeroes=\alpha+\beta=-2$ $product of the zeroes=\alpha\times \beta=1\times (-3)$ $=-3$ $product of the zeroes=\alpha\times \beta=-3$ Then the quadratic equation can be written as $x^2-(-2)x+(-3)=0$ $x^2+2x-3=0$ it is of the form $ax^2+bx+c=0$ COMPARING the 2 EQUATIONS we GET the coefficients a=1 , b=2 and c=-3 The relation between the coefficient and zeroes is $sum of the zeroes=\frac{-b}{a}$ $=\frac{-(2)}{1}$ $=-2$ ∴ sum of the zeroes=-2 $product of the zeroes=\frac{c}{a}$ $=\frac{-3}{1}$ $=-3$ ∴ Product of the zeroes=-3 Hence VERIFIED the relation between the coefficient and zeroes.