Question

write a quadratic with a fractional and irrational solution

Answer 1

got a "a fractional and irrational solution" ?

Answer 2

something like (x-1/2)(x-square root 2)

Answer 3

firstly... get the "solutions" or zeros or roots

get a fractional one
then an irrational one

and you can take it from there easy

Answer 4

they don't have to be specific... just fractional and irrational
pretty much any you can think of

Answer 5

well the zeros can be 1/2 and square root 2..?

Answer 6

sure

Answer 7

i tried multiplying it and u get x^2-sqyare root 2 x -1/2 x -square root 2/x

Answer 8

sqare root 2/2*

Answer 9

so that means to get the polynomial well... the multiplication is right to get the polynomial

Answer 10

\(\bf \begin{cases}
\frac{1}{2}
\\ \quad \\

\sqrt{2}
\end{cases}\left(x-\frac{1}{2}\right)\left(x-\sqrt{2}\right)=\textit{original quadratic polynomial}\)

but you product I think is a bit off

Answer 11

can you help me solve it, i can't get the answer

Answer 12

hmm one sec

Answer 13

\(\bf \begin{cases}
\frac{1}{2}
\\ \quad \\

\sqrt{2}
\end{cases}\left(x-\frac{1}{2}\right)\left(x-\sqrt{2}\right)=x^2+\left({\color{brown}{ -x\sqrt{2}-\frac{1}{2}x}}\right)+\cfrac{\sqrt{2}}{2}
\\ \quad \\

{\color{brown}{ -x\sqrt{2}-\cfrac{1}{2}x\implies \cfrac{-x\sqrt{2}}{1}-\cfrac{x}{2}\implies \cfrac{-2x\sqrt{2}-x}{2}\implies \cfrac{x(-2\sqrt{2}-1)}{2}}}
\\ \quad \\

x^2+\left({\color{brown}{ -x\sqrt{2}-\frac{1}{2}x}}\right)+\cfrac{\sqrt{2}}{2}\implies x^2+\cfrac{x(-2\sqrt{2}-1)}{2}+\cfrac{\sqrt{2}}{2}
\\ \quad \\
x^2-\cfrac{(2\sqrt{2}+1)}{2}x+\cfrac{\sqrt{2}}{2}\)

Answer 14

thank you!

Answer 15

yw