Find the roots of the quadratic equation $a x^{2} + b x + c$ in terms of a, b, c

Open in App

Solution

$a x^{2} + b x + c = 0 (a \neq 0)$

Dividing throughout by a

$x^{2} + \frac{b}{a} x + \frac{c}{a} = 0$

$\Rightarrow (x + \frac{b}{2 a})^{2} - (\frac{b}{2 a})^{2} + \frac{c}{a} = 0$

$\Rightarrow (x + \frac{b}{2 a})^{2} - \frac{b^{2} - 4 a c}{4 a^{2}} = 0$

$\Rightarrow (x + \frac{b}{2 a}) = \pm \sqrt{\frac{b^{2} - 4 a c}{4 a^{2}}}$

$\Rightarrow (x + \frac{b}{2 a}) = \frac{\pm \sqrt{b^{2} - 4 a c}}{2 a}$

x = $\frac{- b}{2 a} \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a}$

x = $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Suggest Corrections

Similar questions

Find the roots of the quadratic equation $a x^{2} + b x + c = 0$ in terms of a, b, c.

x_{1}, x_{2}

a x^{2} + b x + c = 0

c \neq 0

(a x_{1} + b)^{- 2} + (a x_{2} + b)^{- 2}

a, b, c

a x^{2} + b x + c = 0

Zeroes of the quadratic polynomial ax² + bx + c and roots of the quadratic equation ax² + bx + c = 0 are__________

a x^{2} + b x + c = 0

Join BYJU'S Learning Program