Question

Find a quadratic polynomial whose zeros are 1 and -3. Verify the relation between the coefficients and zeros of the polynomial.

Answer 1

given 
  α=1
  β=-3

             (α+β)=(1-3)
                       (-2)
  (αβ)=-3

               quadratic  equation =

                                                 x²-(α+β)x+αβ

      x²+2x-3
by verifing the coeefficients

               -coefficient of x/coeffient of x²
             -2

 nd 

               constant term /coefficient of x²
               -3

Answer 2

Answer:

$\text{the quadratic polynomial is }x^2+2x-3$

Step-by-step explanation:

Given that 1 and -3 are the zeroes of quadratic polynomial.

we have to find the quadratic polynomial and also verify the relation between the coefficients and zeros of the polynomial.

As 1 and -3 are zeroes

∴ (x-1) and (x+3) are factors

⇒ The quadratic polynomial is

$(x-1)(x+3)=x(x+3)-1(x+3)$

                $=x^2+3x-x-3$

                $=x^2+2x-3$

which is required polynomial.

Verification:

$\text{sum of zeroes=}\frac{-b}{a}=\frac{-2}{1}$

$\alpha+\beta=-2$

$1+(-3)=-2$

$-2=-2$    Verified

$\text{product of zeroes=}\frac{c}{a}=\frac{-3}{1}$

$\alpha.\beta=-3$

$1.(-3)=-3$

$-3=-3$     Verified