Question

Find the roots of the equation x2 – 3x – m (m + 3) = 0, where m is a constant

Answer 1

Step-by-step explanation:

x2 – 3x – m(m + 3) = 0

D = b2 – 4ac

D = (- 3)2 – 4(1) [-m(m + 3)]

= 9 + 4m (m + 3)

= 4m2 + 12m + 9 = (2m + 3)2

Important Questions for Class 10 Maths Chapter 4 Quadratic Equations 1

∴ x = m + 3 or -m

Answer 2

$\large\underline{\sf{Solution-}}$

Given quadratic equation is

$\red{\rm :\longmapsto\: {x}^{2} - 3x - m(m + 3)=0}$

can be rewritten as

$\rm :\longmapsto\: {x}^{2} - (3 + m - m)x - m(m +3) = 0$

can be re-arranged as

$\rm :\longmapsto\: {x}^{2} - (m + 3 - m)x - m(m +3) = 0$

$\rm :\longmapsto\: \red{ {x}^{2} - (m + 3)x} + \green{mx - m(m + 3)}=0$

$\rm :\longmapsto\:x\bigg(x - (m + 3) \bigg) + m\bigg(x - (m + 3)\bigg) =0$

$\rm :\longmapsto\:\bigg(x - (m + 3) \bigg)(x + m)=0$

$\rm :\longmapsto\:x =m + 3\: \: \: or \:\:\:x=-\:m$

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac