Question

For what the value of m the equation 3mx square=4(mx-1) will have equal Roots

Answer 1

EXPLANATION.

Value of m the equation,

⇒ 3mx² = 4(mx - 1).

As we know that,

D = Discriminant  b² - 4ac.

D = 0 Roots are real and equal.

⇒ 3mx² = 4(mx - 1).

⇒ 3mx² = 4mx - 4.

⇒ 3mx² - 4mx + 4 = 0.

⇒ (-4m)² - 4(3m)(4) = 0.

⇒ 16m² - 48m = 0.

⇒ 16m(m - 3) = 0.

⇒ m = 0  and  m = 3.

                                                                                                                         

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational an different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

Answer:

m = 0 and m = 3

Step-by-step explanation:

Question:

For what the value of m the equation $\bf{3mx^2=4(mx-1)}$ will have equal Roots?

Solution:

$\rm{3(mx^2)=4(mx-1)}$

$\rm{3mx^2=4mx-4}$

$\rm{3mx^2-4mx+4=0}$

Here,

• a = 3m
• b = -4m
• c = 4

So, as $\rm{3mx^2-4mx+4=0}$ has real and equal roots, their discriminant is 0

D = $\sf{b^2-4ac=0}$

$\sf{(-4m)^2-4(3m)(4)=0}$

$\sf{16m^2-48m=0}$

$\sf{4m^2-12m=0}$

$\sf{m^2-3m=0}$

m = 0 and m = 3