Question

Find a quadratic polynomial whose sum of zeroes is 15 and one zero is -3.
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Answer 1

Answer:

let α and β be the roots of the equation

let us assume that $\alpha =-3$

then

$\alpha +\beta =15$

$-3+\beta =15$

$\beta =18$

As we know, the given quadratic can be written as

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

$x^{2} -x(15)+(-3*18)=0\\x^{2} -15x-54=0$

Answer 2

Step-by-step explanation:

let α and β be the roots of the equation

let us assume that \alpha =-3α=−3

then

\alpha +\beta =15α+β=15

-3+\beta =15−3+β=15

\beta =18β=18

As we know, the given quadratic can be written as

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

2

−x(α+β)+αβ=0

\begin{gathered}x^{2} -x(15)+(-3*18)=0\\x^{2} -15x-54=0\end{gathered}

x

2

−x(15)+(−3∗18)=0

x

2

−15x−54=0