# Find a quadratic polynomial whose sum and product respectively of

Find a quadratic polynomial whose sum and product respectively of the zeroes are as given also find the zeoes of these polynomial by factorization.
(-8/3) , (4/3)
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Hector Roberts
Step 1
Let the roots of a quadratic equation
$a{x}^{2}+bx+c=0$ be $\alpha$ and $\beta$
So, $\alpha +\beta =\frac{-b}{a}=\frac{-8}{3}$...(1)
$\alpha \beta =\frac{c}{a}=\frac{4}{3}$...(2)
$a{x}^{2}+bx+c=0$
$a\left({x}^{2}+\frac{b}{a}x+\frac{c}{a}\right)=0$
Step 2
${x}^{2}-\left(\frac{-b}{a}\right)x+\frac{c}{a}=0$
${x}^{2}-\left(\alpha +\beta \right)x+\alpha \beta =0$
Substitute 1 and 2 in above
${x}^{2}-\left(\frac{-8}{3}\right)x+\frac{4}{3}=0$
$3{x}^{2}+8x+4=0$
$\therefore$ The quadratic equation is $3{x}^{2}+8x+4=0$
Step 3
$3{x}^{2}+8x+4=0$
$3{x}^{2}+2x+6x+4=0$
x(3x+2)+2(3x+2)=0
(3x+2)(x+2)=0
$x=\frac{-2}{3},x=-2$
$\therefore$ The roots are $\frac{-2}{3},-2$