Question

Form the quadratic equation whose roots are 2 and 3

Answer 1

Quadratic equation will be -

x²-(2+3)x + (2×3)
= x²-5x+6

hope this helps :-)

Answer 2

The quadratic equation whose roots are 2 and 3 is x² - 5x + 6 = 0

Given :

The quadratic equation has roots 2 and 3

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 the roots of the quadratic equation

The quadratic equation has roots 2 and 3

Step 2 of 2 :

Find the quadratic equation

The quadratic equation is

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

$\displaystyle \sf{ \implies } {x}^{2} -(2 + 3 )x + (2 \times 3) = 0$

$\displaystyle \sf{ \implies } {x}^{2} -5x + 6= 0$

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