Question

6 gThe product of the roots of the equation 3x2-5mx + (m +5) = 0 is 2 then m' is - (a) tV2 (b) ti (c)Ł1 (d) None of these.​

Answer 1

Answer:

The value of m is 1.

Option c) 1

Step-by-step-explanation:

The given quadratic equation is

3x² - 5mx + ( m + 5 ) = 0.

We have given that,

The product of the roots of the equation is 2.

Comparing the given equation with ax² + bx + c = 0, we get,

• a = 3
• b = - 5m
• c = m + 5

We know that,

$\displaystyle{\boxed{\pink{\sf\:Product\:of\:roots\:=\:\dfrac{c}{a}\:}}}$

$\displaystyle{\implies\sf\:2\:=\:\dfrac{m\:+\:5}{3}}$

$\displaystyle{\implies\sf\:m\:+\:5\:=\:3\:\times\:2}$

$\displaystyle{\implies\sf\:m\:+\:5\:=\:6}$

$\displaystyle{\implies\sf\:m\:=\:6\:-\:5}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:m\:=\:1\:}}}}$

∴ The value of m is 1.

Answer 2

Answer:

Appropriate Question :-

• The product of the roots of the equation 3x² - 5mx + (m + 5) = 0 is 2 then the value of m is :-

Options :

◆ a) 2

◆ b) 3

◆ c) 1

◆ d) None of these

Given :-

• The product of the roots of the equation 3x² - 5mx + (m + 5) = 0 is 2.

To Find :-

• What is the value of m.

Formula Used :-

$\clubsuit$ Product of Roots Formula :

$\bigstar \: \: \sf\boxed{\bold{Product\: Of\: Roots =\: \dfrac{c}{a}}}\: \: \: \bigstar$

Solution :-

Given Equation :

$\mapsto \bf 3x^2 - 5mx + (m + 5) = 0$

By comparing with ax² + bx + c = 0 we get,

❒ a = 3

❒ b = 5m

❒ c = (m + 5)

Now, as we know that :

$\implies \bold{\underline{Product\: Of\: Roots =\: \dfrac{c}{a}}}$

Given :

• Product of roots = 2
• c = (m + 5)
• a = 3

According to the question by using the formula we get,

$\implies \sf Product\: Of\: Roots =\: \dfrac{c}{a}$

$\implies \sf 2 =\: \dfrac{(m + 5)}{3}$

$\implies \sf (m + 5) =\: 2(3)$

$\implies \sf m + 5 =\: 2 \times 3$

$\implies \sf m + 5 =\: 6$

$\implies \sf m =\: 6 - 5$

$\implies \sf\bold{\underline{m =\: 1}}$

$\therefore$ $\sf\boxed{\bold{\underline{The\: value\: of\: m\: is\: 1\: .}}}$

Hence, the correct options is option no (c) 1 .