Question

write the quadratic equation a+b=9 and ab=20​

Answer 1

$\textbf{Concept used:}$

$\text{The quadratic equation having \alpha and \beta as its roots is}$

$\bf\;x^2-(\alpha+\beta)+\alpha\beta=0$

$\textbf{Given:}$

$\text{Sum of the roots=a+b=9}$

$\text{Product of the roots=ab=20}$

$\therefore\text{The required quadratic equation is }$

$x^2-(a+b)x+ab=0$

$\boxed{\bf\;x^2-9x+20=0}$

Find more:

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

(a) x² -18x -16 = 0

(b) x² -18x +16 = 0

(c) x² +18x -16 = 0

(d) x² +18x +16 = 0

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Answer 2

The quadratic equation having α and β as its roots is

(α+β)=9

αβ=20

∴The required quadratic equation is

x²-(a+b)x+ab=0

x²-(9)x+20=0

x²-9x+20=0

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Hope this helped