Question

Find the value of m for which the root of the equation mx(6x+10)+25=0 are equal.​

Answer 1

EXPLANATION.

Equation ⇒ mx(6x + 10) + 25 = 0.

⇒ f(x) = mx(6x + 10) + 25.

⇒ 6mx² + 10mx + 25 = 0.

As we know that,

Discriminant = D.

D = b² - 4ac.

For real and equal roots,

D = 0  Or  b² - 4ac = 0.

⇒ (10m)² - 4(6m)(25) = 0.

⇒ 100m² - 600m = 0.

⇒ 100m(m - 6) = 0.

⇒ m = 0  or  m = 6.

                                                                                         

MORE INFORMATION.

Nature of the factors of the quadratic expression,

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

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

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

(4) = imaginary, if D < 0.

Answer 2

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Equation is → mx (6x + 10 ) + 25 = 0

Solving furthur we get..

→ mx(6x) + mx(10) + 25 = 0

→ 6mx² + 10mx + 25 = 0

________________

For equal roots,Discriminant(D) = 0

D = b² - 4ac = 0

Here ,

• a = 6m

• b = 10m

• c = 25

Putting values we get...

(10m)² - 4(6m)(25) = 0

100m² - 600m = 0

100m( m - 6 ) = 0

100m = 0 ㅤㅤㅤㅤㅤㅤㅤ m-6 = 0

m = 0 or 6

Hence , value of m is 0 or 6.