Question

Find zero of the quadratic polynomials F(x)=x2/a+b/ac*x/b_1/c

Answer 1

Given:

The quadratic polynomials F(x)=x2/a+b/ac*x/b_1/c

To find:

Find zero of the quadratic polynomials F(x)=x2/a+b/ac*x/b_1/c

Solution:

Given quadratic polynomial,

$F(x)=\dfrac{x^2}{a} + \dfrac{b}{ac} \times \dfrac{x}{b}-\dfrac{1}{c}$

Given equation is a quadratic equation.

The roots of a quadratic equation are given as follows.

For an equation, ax² + bx + c = 0

The roots are given by,

$x = \dfrac{-b \pm \sqrt {b^2-4ac}}{2a}$

$F(x)=\dfrac{x^2}{a} + \dfrac{b}{ac} \times \dfrac{x}{b}-\dfrac{1}{c}$

Equating the above equation to zero and solving it, we get

$0=\dfrac{x^2}{a}+\dfrac{b}{ac}\times \dfrac{x}{b}-\dfrac{1}{c}$

$bcx^2+bx-ab=0$

$x=\dfrac{-b+\sqrt{b^2-4bc\left(-ab\right)}}{2bc}:\quad \dfrac{-1+\sqrt{4ac+1}}{2c}\\\\\x=\dfrac{-b-\sqrt{b^2-4bc\left(-ab\right)}}{2bc}:\quad -\dfrac{\sqrt{4ac+1}+1}{2c}$

Therefore the roots of a given polynomial equation are:

$x=\dfrac{-1+\sqrt{4ac+1}}{2c},\:x=-\dfrac{\sqrt{4ac+1}+1}{2c};\quad \:b\ne \:0,\:c\ne \:0$