Question

Write the quadratic equation, if the sum of the roots is 10 and the product of the roots is 9.​

Answer 1

Answer:

$by \: the \: formula \: of \: quadratic \: equation$

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

$x {}^{2} - 10x + 9$

Answer 2

The quadratic equation is x² - 10x + 9 = 0

Given :

The sum of the roots is 10 and the product of the roots is 9.

To find :

The quadratic equation

Concept :

If the Sum of zeroes and Product of the zeroes of a quadratic equation is given then the quadratic equation is

$\sf {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes = 0$

Solution :

Step 1 of 2 :

Write down sum of the roots and the product of the roots

Here it is given that sum of the roots is 10 and the product of the roots is 9.

Step 2 of 2 :

Find the quadratic equation

The quadratic equation is given by

$\sf {x}^{2} -(Sum \: of \: the \: roots )x + Product \: of \: the \: roots = 0$

$\displaystyle \sf\implies {x}^{2} -10x + 9 = 0$

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