Name: Factorisation Method of Solving Quadratic Equations
Uploaded: 2019-07-19
Duration: 6 min 30 s
Description: In this video, we will learn the method of factorisation and find the roots of quadratic equations by the factorisation method in detail.

Question

Find the value(s) of $m$ for which the following quadratic equation has real and equal roots:

$(3 m + 1) x^{2} + 2 (m + 1) x + m = 0$

Accepted Answer

In the quadratic equation $a x^{2} + b x + c = 0$ , where $a, b, c$ are real numbers and $a \neq 0$ , the discriminant is given by $D = b^{2} - 4 a c$ .

We know that if a equation has real and equal roots, its discriminant is $0$

The given quadratic equation is $(3 m + 1) x^{2} + 2 (m + 1) x + m = 0$ . Comparing this equation with the equation $a x^{2} + b x + c = 0$ , we obtain, $a = (3 m + 1) b = 2 (m + 1)$ and $c = m$ .

Thus, we have, $b^{2} - 4 a c = 0$

$\Rightarrow {[2 (m + 1)]}^{2} - 4 \times (3 m + 1) \times m = 0$

$\Rightarrow 4 (m^{2} + 2 m + 1) - 4 \times (3 m^{2} + m) = 0$

$\Rightarrow m^{2} + 2 m + 1 - (3 m^{2} + m) = 0$

$\Rightarrow m^{2} + 2 m + 1 - 3 m^{2} - m = 0$

$\Rightarrow - 2 m^{2} + m + 1 = 0$

$\Rightarrow 2 m^{2} - m - 1 = 0$

$\Rightarrow 2 m^{2} - 2 m + m - 1 = 0$

$\Rightarrow 2 m (m - 1) + (m - 1) = 0$

$\Rightarrow (m - 1) (2 m + 1) = 0$

$\Rightarrow m - 1 = 0$ or $2 m + 1 = 0$

$\Rightarrow m = 1$ or $m = - \frac{1}{2}$

Therefore, the required value of $m$ is $1$ or $- \frac{1}{2}$ .

Find the value(s) of $m$ for which the following quadratic equation has real and equal roots:

$(3 m + 1) x^{2} + 2 (m + 1) x + m = 0$

Important Questions on Quadratic Equations in One Variable

Learn and Prepare for any exam you want !

Find the value(s) of m for which the following quadratic equation has real and equal roots: 3m+1x2+2m+1x+m=0

Important Questions on Quadratic Equations in One Variable

Learn and Prepare for any exam you want !

Find the value(s) of $m$ for which the following quadratic equation has real and equal roots:

$(3 m + 1) x^{2} + 2 (m + 1) x + m = 0$