Question

5. Find the discriminant of 15x2 = 4x – 1 and describe
the nature of the roots of the equation. Then solve the
equation by using the Quadratic Formula.

Answer 1

Answer:

a) The discriminant of the equation =  - 44

b)The nature of the roots will be imaginary.

c) $x = \frac{2 +\sqrt{11} i}{15}  or, x = \frac{2 - \sqrt{11} i}{15}$

Step-by-step explanation:

Here, the given expression is $15x^{2}  = 4x -1$

or, $15x^{2}  -  4x + 1   = 0$

Now the discriminant (D) of a quadratic equation $ax^{2}  +b x + c   = 0$

D = $b^{2}   -  4ac  = (-4)^{2}  -  4(15) (1)  = 16 - (60) = -44$

Hence, the discriminant of the equation =  - 44

As D< 0, so the roots will be imaginary.

Now,by quadratic formula : $x = \frac{-b \pm \sqrt{b^{2}  - 4ac} }{2a}$

So, here $x = \frac{-(-4) \pm \sqrt{D} }{2a}  = \frac{4 \pm \sqrt{(-44 )} }{30}$

So, either $x = \frac{4 + \sqrt{(-44 )} }{30} or, x =  \frac{4 - \sqrt{(-44 )} }{30}$

or, $x = \frac{2 +\sqrt{11} i}{15}  or, x = \frac{2 - \sqrt{11} i}{15}$