Question

For a quadratic equation in variable 'm', the coefficients a, b and care such that a = 2, b = 4a, c = 3a. Form the quadratic equation and solve it by factorisation method. ​

Answer 1

Step-by-step explanation:

ax2 + bx + c = 0

For equal roots D = 0

⇒ b2 = 4ac

Case I : ac = 1

(a, b, c) = (1, 2, 1)

Case II : ac = 4

(a, b, c) = (1, 4, 4)

or (4, 4, 1)

or (2, 4, 2)

Case III : ac = 9

(a, b, c) = (3, 6, 3)

Required probability = 5/216

Answer 2

Answer:

The required quadratic equation is found to be: $m^2+4m+3=0$ and its zeroes are found to be $-1,-3$.

Step-by-step explanation:

We know that the general form of a quadratic equation is given by:

$ax^2+bx+c=0$

As we have to formulate an equation in variable 'm', we will replace x by m.

Replacing x by m, we get:

$am^2+bm+c=0$

Also, we are given that $a=2$, $b=4a$ and $c=3a$,

Substituting the value of a in b, we get:

$b=4(2)$

$b=8$

Similarly, for c:

$c=3(2)$

$c=6$

Substituting a, b and c in the general form of an equation in variable 'm',

$2m^2+8m+6=0$

Taking 2 common, we get:

$m^2+4m+3=0$

Now, factorising it, we get:

$m^2+3m+m+3=0$

$m(m+3)+1(m+3)=0$

$(m+3)(m+1)=0$

So, the zeroes of the equation are:

$m=-1,-3$