1 Answer

Turque · Answer 1 · 2023-04-25T01:18:59+0000

Given the equation:

$4x^2-12=3x\text{ ----- equation 1}$

Required: sum and product of the roots of the equation

solution:

For a quadratic equation of the form

$ax^2\text{ + bx + c = 0 ------ equation 2}$

the sum of the roots is expressed as

$\text{sum of roots = -}(b)/(a)$

the product of the roots is expressed as

$\text{product of roots = }(c)/(a)$

The given quadratic equation can be rewritten in the form as in equation 2 to be

$4x^2-3x-12\text{ = 0 ----- equation 3}$

In comparison to equation 2,

$\begin{gathered} a\text{ = 4} \\ b\text{ = -3} \\ c\text{ =-12} \end{gathered}$

Thus,

Sum of roots:

$\begin{gathered} \text{sum of roots = -}(b)/(a) \\ =-(-3)/(4) \\ =(3)/(4) \end{gathered}$

thus, the sum of the roots is

Products of roots:

$\begin{gathered} \text{product of roots = }(c)/(a) \\ =(-12)/(4) \\ =-3 \end{gathered}$

thus, the product of the roots is

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