Question

If the sum of the roots of the quadratic equation is 12 and their product is 32. Find the equation.​

Answer 1

Answer:

The Equation Will be:

x²-(Sum of the Zeroes)x+Product of the Zeroes.

Putting the Values,

=x²-(12)x+(32).

=x²-12x+32.

Answer 2

Answer:

Required equation is ${x}^{2} - 12x + 32 = 0$

Step-by-step explanation:

Given,the sum of the roots of the quadratic equation is 12 and their product is 32.

We know if $a {x}^{2} + bx + c = 0$ is a equation then sum of roots of the equation is $(- \frac{b}{a})$

and product of roots of the equation is $\frac{c}{a}$

We also know that,

If $\alpha \: and \: \beta$ are two roots of a equation then the equation is ${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0....(2)$

Where $( \alpha + \beta )$ is sum of two roots and $\alpha \beta$ is product of two roots.

According to question,

$\alpha + \beta = 12 \\ \alpha \beta = 32$

So, required equation is ${x}^{2} - 12x + 32 = 0$

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