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$57$ x^ $2$ +( $57$ b+a)+ab= $0$ In the given solution, a and b are constants. The product of the solutions to the given equation is kab, where k is a constant. what is the value of k? $\newline$ a) $1$ / $57$ $\newline$ b) $1$ / $19$ $\newline$ c) $1$ $\newline$ d) $57$

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Simplify radical expressions with variables

Full solution

Q.

57

x^

2

+(

57

b+a)+ab=

0

In the given solution, a and b are constants. The product of the solutions to the given equation is kab, where k is a constant. what is the value of k?

\newline

a)

1

/

57

\newline

b)

1

/

19

\newline

c)

1

\newline

d)

57

Identify the quadratic equation: Identify the quadratic equation: $57x^2 + (57b + a)x + ab = 0$ .
Use quadratic formula properties: Use the quadratic formula properties. The product of the roots of $ax^2 + bx + c = 0$ is given by $\frac{c}{a}$ .
Calculate product of roots: Here, $a = 57$ , $b = 57b + a$ , and $c = ab$ . So, the product of the roots is $\frac{ab}{57}$ .
Find value of k: Given that the product of the solutions is $kab$ , we have $\frac{ab}{57} = kab$ .
Solve for k: Solve for $k$ : $k = \frac{1}{57}$ .

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