Question

Plz solve this.
Find the value of m in the eq.
3x^2+mx+2=0
if the roots are equal.
Also find the roots of the Equation.
Not for Mother#$&*er spammers. ​

Answer 1

Let the roots be = a and b

a × b = 2/3 [product of roots = c/a]

=> a = _/(2/3) [roots are equal]

a + b = m/3 [sum of roots = -b/a]

=> _/(2/3) × 2 = m/3

=> 2_/(2/3) × 3 = m

=> 2_/6 = m

Thus, m is equal to 2_/6

Note:- "_/" represents square roots sign.

Answer 2

Solution :-

$3 {x}^{2} + mx + 2 = 0 \\ compare \: equation \: with \: a {x}^{2} + bx + c = 0 \\ a = 3, \: b = m ,\: c = 2 \\ the \: roots \: are \: equal. \\ {b}^{2} - 4ac = 0 \\ {m}^{2} - 4 \times 3 \times 2 = 0 \\ {m}^{2} - 24 = 0 \\ {m}^{2} = 24 \\ m = \sqrt{24} \\ m = \sqrt{4 \times 6} \\ m = 2 \sqrt{6}$