(-8/3) , (4/3)

lugreget9
2021-12-17
Answered

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)

(-8/3) , (4/3)

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Hector Roberts

Answered 2021-12-18
Author has **31** answers

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)

$a{x}^{2}+bx+c=0$

$a({x}^{2}+\frac{b}{a}x+\frac{c}{a})=0$

Step 2

${x}^{2}-\left(\frac{-b}{a}\right)x+\frac{c}{a}=0$

${x}^{2}-(\alpha +\beta )x+\alpha \beta =0$

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 $\frac{-2}{3},-2$

Let the roots of a quadratic equation

So,

Step 2

Substitute 1 and 2 in above

Step 3

x(3x+2)+2(3x+2)=0

(3x+2)(x+2)=0

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