Question

Solve the quadratic equation using formula method.m(3m+1)=2

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Answer 1

Answer:

m(3m + 1 )= 2

= 4m +1m =2

= 5m =2

m=5/2 or m=2.5

Answer 2

Given

• A equation m(3m+1)=2

To Find

• value of m or root of the equation

Concept used

Discriminant

$\bf \: d = {b}^{2} - 4ac$

Quadratic formula

$\bf \: x = \dfrac{ - b \pm \sqrt{d} }{2a}$

Solution

1. First we made equation in the form of quadratic equation

$\rm \: m(3m + 1) = 2 \\ \\ \implies \boxed{ \bf \: 3 {m}^{2} + m - 2 = 0 }$

2. Now we have quadratic equation

3. here

• a=3
• b=1
• c=-2
• $\rm \: d = {b}^{2} - 4ac \\ \\ \implies \rm \: d = {1}^{2} - 4 \times 3 \times - 2 \\ \\ \implies \rm \: d = 25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now

Using Quadratic Formula

$\rm \: x = \dfrac{ - b \pm \sqrt{d} }{2a}$

4. Here x(root) of this equation is m so we solve it now

5. Putting values

$\rm \: m = \dfrac{ - 1 \pm \sqrt{25} }{2 \times 3} \: \: \: \: \: \: \: \\ \\ \implies \rm \: m = \dfrac{ - 1 \pm \: 5}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \rm \: m = \frac{ - 1 + 5}{6} \: \: \: or \: \frac{ - 1 - 5}{6} \: \\ \\ \implies \rm \: m = \frac{4}{6} \: \: or \: \frac{ - 6}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \underline{ \boxed{ \huge \bf \: m = \frac{2}{3} \: or \: - 1}}$

We can conclude that both roots are 2/3 or -1 you can do this question with middle term split also

Alternative method

Middle term split

$\rm \: 3 {m}^{2} + m - 2 = 0 \\ \\ \implies \rm \: 3 {m}^{2} + 3m - 2m - 2 = 0 \: \: \: \: \: \: \\ \\ \implies \rm \: 3m(m + 1) - 2(m + 1) \: \: \: \: \: \: \: \: \: \: \\ \\ \rm \implies (m + 1) = 0 \: or \: (3m - 2) = 0 \\ \\ \implies \underline{ \boxed{ \huge \bf \: m = - 1 \: or \: \frac{2}{3} }}$

Hence it is also verified by this method that the roots of this equation is -1 or 2/3