Question

The quadratic equation whose roots are –2 and 4 is given by
​

Answer 1

Answer:

the quadretic equation whose roots are -2 and 4 is

(x+2).(x-4)=0

x^2+2x-4x-8=0

x^2-2x-8=0

Answer 2

The required quadratic equation whose roots are - 2 and 4 is x² - 2x - 8 = 0

Given :

A quadratic equation whose roots are - 2 and 4

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 - 2 and 4

Sum of roots = - 2 + 4 = 2

Product of the roots = - 2 × 4 = - 8

Step 2 of 2 :

Find the quadratic equation

The required quadratic equation is given by

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

$\displaystyle \sf \implies {x}^{2} - (2)x + (-8) = 0$

$\displaystyle \sf \implies {x}^{2} - 2x - 8 = 0$

Hence the required quadratic equation whose roots are - 2 and 4 is x² - 2x - 8 = 0

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If p(x) = 2x2 + 4x + 6 is a quadratic polynomial then what is the value of sum of zeroes?

https://brainly.in/question/31024345

2. write a quadratic polynomial sum of whose zeroes is 2 and product is -8

https://brainly.in/question/25501039