Question

the roots of a quadratic equation are 1,3 what is the equation​

Answer 1

sum= 1+3 = 4

product = 1×3 = 3

x^2 -( sum)x + product

x^2-4x + 3

Answer 2

The quadratic equation whose roots are 1 and 3 is x² - 4x + 3 = 0

Given :

A quadratic equation whose roots are 1 and 3

To find :

The quadratic equation

Concept :

If the roots of a quadratic equation is given then the quadratic equation is given by

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

Solution :

Step 1 of 2 :

Find Sum of roots and Product of the roots

Here it is given for a quadratic equation whose roots are 1 and 3

Sum of roots = 1 + 3 = 4

Product of the roots = 1 × 3 = 3

Step 2 of 2 :

Find the quadratic equation

The required quadratic equation is given by

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

$\displaystyle \sf \implies {x}^{2} - 4x + 3 = 0$

Hence the quadratic equation whose roots are 1 and 3 is x² - 4x + 3 = 0

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