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Write the quadratic equation whose roots are 4 and 6, and whose leading coefficient is 2

(Use the letter x to represent the variable)

Respuesta :

ivana2103
Theres a formula with quadatic equations which goes: “a(x-x1)(x-x2)” where x is.. well, “x”, x1 and x2 are the roots and a is the leading coefficient.

So our formula would be 2(x-4)(x-6), and if we multiply all that we get:

2x^2-12x-8x+48=
= 2x^2-20x+48 is our eqtn (if I didn’t get anything wrong, of course)
deepakrai138

The required quadratic equation is [tex]2x^{2} -20x+48[/tex].

Given roots of quadratic equation are 4 and 6.

Also given here leading coefficient is 2.

We know that, the formulae for forming quadratic equation when its roots are given is as follows: [tex]x^{2} -(\alpha +\beta )x+\alpha \beta[/tex]

Here [tex]\alpha and \beta[/tex] are the roots of the quadratic equation.

Let [tex]\alpha =4 and \beta = 6[/tex]

Putting the value of [tex]\alpha and\beta[/tex] in the above formulae we get,

[tex]x^{2} -(4+6)x+4\times6[/tex]

[tex]x^{2} -10x+24[/tex]

But remember here 2 is the leading coefficient of the quadratic equation with roots 4 and 6 (given in question),so we have to multiply the equation by 2 to get the final answer.

So, [tex]2(x^{2} -10x+24)[/tex]

[tex]2x^{2} -20x+48[/tex].

Hence the required quadratic equation is [tex]2x^{2} -20x+48[/tex].

For more details on quadratic equation follow the link:

https://brainly.com/question/2263981

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