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57x^(2)+(57 b+a)x+ab=0
In the given equation,
a and
b are positive constants. The product of the solutions to the given equation is
kab, where
k is a constant. What is the value of
k ?
A.
(1)/(57)
B.
(1)/(19)
C. 1
D. 57

$57 x^{2}+(57 b+a) x+a b=0$ $\newline$ In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $k a b$ , where $k$ is a constant. What is the value of $k$ ? $\newline$ A. $\frac{1}{57}$ $\newline$ B. $\frac{1}{19}$ $\newline$ C. $1$ $\newline$ D. $57$

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Simplify radical expressions with variables

Full solution

Q.

57 x^{2}+(57 b+a) x+a b=0

\newline

In the given equation,

a

and

b

are positive constants. The product of the solutions to the given equation is

k a b

, where

k

is a constant. What is the value of

k

?

\newline

A.

\frac{1}{57}

\newline

B.

\frac{1}{19}

\newline

C.

1

\newline

D.

57

Identify Form: Identify the form of the quadratic equation and relate it to the standard form $ax^2 + bx + c = 0$ .
Use Vieta's Formulas: Use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. For a quadratic equation $ax^2 + bx + c = 0$ , the product of the roots is given by $\frac{c}{a}$ .
Compare Roots Product: Compare the product of the roots to the given form $kab$ .
Solve for $k$ : Solve for $k$ .
Match Value of $k$ : Match the value of $k$ with the provided options.

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