Question

Write the quadratic equation whose roots are -1 and -4

Answer 1

Roots are - 1 and - 4

Sum of roots = - 1 - 4 = - 5

Product of roots = (-1)(-4) =4

Required equation is
x^2 - (sum of roots) x + Product of roots = 0
=> x^2 - (-5)x +4 =0
=> x^2 +5x + 4 = 0

Answer 2

The required quadratic equation whose roots are - 1 , - 4 is x² + 5x + 4 = 0

Given :

The roots of the quadratic equation are - 1 , - 4

To find :

The quadratic equation

Concept :

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

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

Solution :

Step 1 of 2 :

Find Sum of zeroes and Product of the roots

Here it is given that roots of the quadratic equation are - 1 , - 4

Sum of the roots

= ( - 1 ) + ( - 4 )

= - 1 - 4

= - 5

Product of the roots

= ( - 1 ) × ( - 4 )

= 4

Step 2 of 2 :

Find the quadratic equation

The required quadratic equation is

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

$\displaystyle \sf{ \implies {x}^{2} - ( - 5)x + 4 = 0}$

$\displaystyle \sf{ \implies {x}^{2} + 5x + 4 = 0}$

Hence the required quadratic equation whose roots are - 1 , - 4 is x² + 5x + 4 = 0

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