Question

if the root of equation x^2+kx+24=0 are in the ratio 2:3 then k=

Answer 1

Plz find the attachment

Answer 2

Answer:

Step-by-step explanation:

Concept:

A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:

ax² + bx + c = 0

where a, b, and c are constant terms and x is the unknown variable.

The quadratic is referred to as univariate because there is just one unknown term or variable. The equation is a polynomial equation, with 2 being the largest power, because the powers of the variable x are always non-negative integers.

The values of x, commonly known as zeros, are the answer to this equation. The answer for which the equation is satisfied is the polynomial's zeros. There are two roots, or zeros, to the equation for quadratics. Additionally, the left-hand side of the equation will equal zero if we put the values of the roots of x there. They are known as zeros as a result.

Given:

equation $=x^2+kx+24$

roots of the equation are in the ratio is $2:3$

product of the roots $= 24$

Sum of the roots $=-k$

Find:

the value of k

Solution:

Given equation $=x^ 2+kx+24$

The roots of the equation are in the ratio is $2:3$

Let the roots be $2a$ and $3a$

$\alpha =2a$

$\beta =3a$

Sum of the roots $=\alpha +\beta$

                            $-k=2a+3a$

                            $-k=5a$

Product of the roots $=\alpha \beta$

                                 $24=(2a)(3a)$

                                 $24=6a^2$

                                 $a^ 2=4$

                                 $a=2, a=-2$

put the value of $a=2$ in $k$

                             $-k=5(2)$

                             $k=-10$

put the value of $a=-2$  in $k$

                               $-k=5(-2)$

                               $k=10$

Hence k=10 and k=-10

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