Question

Given the sum and the products of the roots of the quadratic equation 3x^2 + hx + k = 0 are 10/3 and -3/8 respectively, find the values of h and k and the quadratic equation with roots h and k.

Answer 1

Step-by-step explanation:

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Answer 2

Concept: A quadratic equation can be defined as; $ax^{2}+bx +c=0$,  where a, b, and c are known and 'x' is variable. If $\alpha$ and $\beta$ will be two roots of the quadratic equation, then $\alpha$ and $\beta$ is given by

$\alpha +\beta = -\frac{b}{a}$   and  $\alpha *\beta =\frac{c}{a}$

Given: The sum and the products of the roots of the $3x^{2} +hx+k=0$ $3x^{2} +hx+k=0$ are $\frac{10}{3}$ , $-\frac{3}{8}$ respectively

To Find: Find the values of h and k and the quadratic equation with roots h and k.

Solution:

In the question $3x^{2} +hx+k=0$

The sum of the roots is $\frac{10}{3}$ = $-\frac{h}{3}$ ,

                                $h=-10$

Product of roots is $-\frac{3}{8}=\frac{k}{3}$

                                 $k= -\frac{9}{8}$

Now put this value in a given equation

$3x^{2} -10x-\frac{9}{8} =0$

$24x^{2} -80x-9=0$

Hence the value of h = -10, the value of k= $-\frac{9}{8}$ and the equation is

$24x^{2} -80x-9=0$