Question

What is the discriminant of the quadratic equation  4y2+y−16=0?​

Answer 1

Answer:

257

Step-by-step explanation:

The discriminant of a quadratic equation is = b² - 4 ac

a=4

b=1

c=-16

Therefore:

b²- 4ac= 1²-4(4) (-16)

           = 1+ 256

           = 257

Ans: 257

Answer 2

Answer:

The discriminant of the quadratic equation is 257.

Step-by-step explanation:

Here given equation is $4 {y}^{2} + y - 16 = 0....(1)$

Here we want to find discriminant of this quadratic equation.

If $a {x}^{2} + bx + c = 0$

is a quadratic equation then discriminant of this equation is ${b}^{2} - 4ac$

By one example we can understand this concept easily.

Let a equation be ${x}^{2} - 2x + 1 = 0....(2)$

First we are comparing equation (2) with equation $a{x}^{2} + bx + c = 0$

and get,

$a = 1 \\ b = - 2 \\ c = 1$

Now discriminant

$= {b}^{2} - 4ac$

$= {( - 2)}^{2} - 4 \times 1 \times 1$

$= 4 - 4 = 0$

Discriminant of equation (2) is 0.

Now we are Comparing equation (1) with equation

$a {y}^{2} + by + c = 0$

$a = 4 \\ b = 1 \\ c = - 16$

So required discriminant${b}^{2} - 4ac = {1}^{2} - 4 \times 4 \times ( - 16) = 1 + 256 = 257$