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Nutka1998 [239]
3 years ago
8

5. Find the discriminant of 15x2 = 4x – 1 and describe

Mathematics
1 answer:
diamong [38]3 years ago
8 0

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}

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