Question

The no of roots of the quadratic equation 8sec2theta - 6sec theta +1=0 is

Answer 1

Consider the given equation,

$8\sec^{2}\Theta -6\sec \Theta +1=0$

Let $\sec\Theta=x$,

so the equation becomes as

$8x^{2}-6x+1=0$

Now, we will find the roots of the above equation.

$Discriminant(D)=b^{2}-4ac$

$D=6^{2}-(4 \times 8)$

$D=36-32 = 4$

The roots are calculated by the formula $x= \frac{-b\pm \sqrt{D}}{2a}$

$x= \frac{6\pm \sqrt{4}}{16}$

$x= \frac{6\pm 2}{16}$

$x= \frac{8}{16}$ and $x= \frac{4}{16}$

x= $\frac{1}{2}$ and $x= \frac{1}{4}$

Since, $\sec \Theta =x = \frac{1}{2}=\frac{1}{4}$

So, there are 2 roots for the given equation.

Answer 2

Answer:No solution exist.

Step-by-step explanation: