Question

20.Solve 8x^(4)+4x^(3)-18x^(2)+11x-2=0, given that it has equal roots.​

Answer 1

Given:

Equation: 8x⁴ + 4x³ - 18x² + 11x - 2 = 0

To find:

Roots of the equation

Solution:

8x⁴ + 4x³ - 18x² + 11x - 2 = 0

We will apply rational root theorem to solve the given equation.

By the theorem,

If constant term of the equation = p

And coefficient of highest degree term = q

Then the rational roots of the given equations will be in the form of $\frac{a}{b}$.

Here a = factors of p

b = factors of q

Possible rational roots = $\frac{\pm1,\pm2}{\pm1,\pm2,\pm4,\pm8}$              

                                     ≈ $\pm1,\pm{\frac{1}{2}},\pm\frac{1}{4},\pm\frac{1}{8},\pm2,$

Out of these roots if we put each value in the equation then we find only two roots which satisfy the equation.

x = $\frac{1}{2}, -2$

For x = 0.5,

8(0.5)⁴+ 4(0.5)³- 18(0.5)² + 11(0.5) - 2

= 0.5 + 0.5 - 4.5 + 5.5 - 2

= 6.5 - 6.5

= 0

For x = -2,

8(-2)⁴+ 4(-2)³- 18(-2)²+ 11(-2) - 2

= 128 - 32 - 72 - 22 - 2

= 0  

Therefore, there are only two solutions of the given equation.

x = 0.5, -2